The Carbon Dioxide System in the Oceans B y RICARDO M. PYTKOWlCZ Oregon State University, Corvallis, Oregon, USA Manuscript received 23 January 1973

ABSTRACT A model of the carbon dioxide system in nature is derived and is used to further our understanding of the factors which control this system in the oceans, the atmosphere, and the sediments.

The qualitative model The first step in obtaining a model of the C02 system is to select the minimum numbers of reservoirs and fluxes needed to represent it. The selection of reservoirs is not unique and is biased b y the problem on hand. We seek general geochemical description and, to prevent the diagram from becoming unmanageable, will not subdivide the oceans into water masses, look at individual mineral phases of carbonates, or consider biological speciation or trophic levels. The diagram of the CO s system is presented in Figure 1. The primary input into the atmosphere is the juvenile CO s which is produced b y the degassing of the mantle, and which is taken up b y biological and geological processes on and in the crust and b y the oceans. The crustal uptake is represented b y flux JvA-~, the flux from reservoir 1 to 2 via photosynthesis at A. The resulting organic carbon (org-C) m a y be lithified (Jr6), transported to the oceans as dissolved and particulate organic (Jvc-8) or m a y be oxidized back to CO v The soil solution is usually supersaturated with COs and part of its COs content returns to the atmosphere (J3-1). The remainder is used to weather aluminium silicates at D and sedimentary carbonates at E. The weathering reactions m a y be illustrated b y the generic equations (GARRELS [1]) 2NaA1Si30s + 2C02 + 3H20 ~ 2Na+ + 2HCO~ + A12SiaOs(OH)4 + 4SiO 2

(1)

and by CaxMgl_zCO 3 + CO~ + H20 ~ xCa ~+ + (1-x)Mg ~+ + (1-x)Mg 2+ + 2HCO~.

(2)

35/1, 1973

Carbon Dioxide System in Oceans

9

The HCOs formed by the above reactions is transported to the oceans by rivers (JD-T and Jg_v) and becomes part of the total dissolved inorganic carbon dioxide of seawater TCO, = (CO,) + (H~C03) + (HCO;) + (CO~-). (3)

[ATMOSPHERE]

auv.CO;~

coz

coz coz

; ~

or(i-C

,I-'~Or;LI-C ~-c

B

~-c

HCO3

COz J

F

"Z

%

HC03

LHr Org-C

__ ~

"I'C03[ Tes~$r

N

C03 C05

CO~

0~9-C Fig. 1. A block diagram of the CO2 system. i A B C D E F G H I J K L M N

The symbols have the following meaning: Photosynthesis on land 1 Atmospheric CO 2 2 Organic carbon on land Oxidation on land 3 Dissolved inorganic carbon on land Physical weathering of organic carbon 4 CO S content of aluminium silicates Weathering of aluminium silicates 5 Sedimentary carbonates Weathering of carbonates 6 Lithified organic carbon Photosynthesis in the oceans 7 Dissolved inorganic carbon in the oceans Oxidation in the oceans 8 Organic carbon in the oceans Formation of calcareous tests 9 Calcareous tests plus detrital carbonateq Dissolution of tests 10 Carbonate sink Junction 11 Organic carbon sink Junction Junction Metamorphism Physical weathering of CaCO 3

10

I~. Pytkowicz

Hydrologie

The HCO- which results from the waethering of sedimentary carbonates is removed by calcareous tests at H, by the reverse of reaction (2). The CO s generated, which corresponds to the atmospheric COs used in the weathering, is returned to reservoir 7 by J~.~ and eventually re-enters the atmosphere. A stations_ry (time-invariant) condition exists if biological utilization by tests equals the weathering rate. Inorganic precipitation of CaCOs was not mentioned because P~rKOWlCZ C21 showed that the removal of carbonates from the open oceans is strictly biogenic. More than half of the settling or settled tests are redissolved at I by reacting with CO s resulting from the oxidation of organic matter E3, 4, 51. At least part of the remaining CaCOs, which is incorporated into the submarine sediments (JvJ) is eventually returned to the weathering environments on the continents E6~ by flux J~-5 but some of it may be permanently removed into reservoir 10. This point as well as others left unanswered in this section will be discussed in the next one. Reaction (1) does not describe the weathering of all igneous rock types. An important role is played by plagioclase feldspars, which may be weathered b y reactions such as CaAI~Si20 v 2NaA1Si30 a + 4H2CO s + 2(nH20) Ca2+ + 2Na+ + 3HCO~ + 2Al~(OH)2Si4010 9nHzO. (4) Calcium bearing igneous rocks will be represented for simplicity by 'Calg' in the remainder of this text. The Ca(HCOs) ~generated by reaction (4) is utilized b y calcareous organisms in the same way as the product of reaction (2) and part of the resulting CaC03 may form new carbonate rocks. The weathering of Calg probably was the original source of most carbonate rocks. The remaining CaCO.~may eventually be brought by sea-floor spreading to metamorphic environments where it can undergo reactions of the general type CaC03 + SiOl = CaSi03 + COl (at M in Fig. 1) and be brought by tectonic activity back to reservoir 5. The C02 released during metamorphism is returned to the atmosphere (JM-1). The weathering of Nalg and Klg yields soluble NaHCOa and KHCO 3 which must undergo reverse weathering if the oceans are not to become soda lakes. The C02 released by reverse weathering is represented as joining J~-v This topic will be discussed further later on. The organic carbon cycle will be examined next. It has been pointed out by GARRELSand MACKENZIE[8] that photosynthesis exceeds oxidation on land and that the surplus org-C is transported to the oceans by rivers (J~-c-8). The primary supply of org-C to reservoir 8 comes from photosynthesis at F. Most of the org-C is oxidized and returns to 7 by JvG-7- Some of the CO,, produced by oxidation is used in the dissolution of calcareous tests in deep waters (Ja-I), as was mentioned earlier. That part of the org-C which is not oxidized settles to the sediments, is eventually lithified, and either joins the weathering reservoir (flux JL-6) or is removed into sink 11, depending upon whether the system is entirely cyclic or n.ot. The material in reservoir 6 Call be physically weathered (Je-c) or it can be oxidized (J6.B). It will be shown later that Jl-~ and J~-v the exchange fluxes between the atmosphere and the oceans, are not equal as the excess of photosynthesis over oxidation on land is compensated by net outflows of C02 into the atmosphere and, as org-C, into the sediments. Thus, surface seawaters are, on the average, slightly supersatu-

35/1, 1973

Carbon Dioxide System in Oceans

11

rated with COs resulting from oxidation in and upwelling of deep waters. This supersaturation occurs primarily at low latitudes (SKIRROW [9]) possibly because the saturation level is further enhanced by the warming of the waters and the decrease in pH following biogenic removal of CaCO 3. It has been shown in this section that the COs system in nature, although extremely complex, can be represented for geochemical purposes by 11 reservoirs and 30 fluxes. This large number of interconnected reservoirs must be kept in mind during studies of consequences of fossil fuel burning but, surprisingly, has been ignored by most workers in the field. The flow chart presented in Figure 1 Hill be helpful in the discussion that follows.

A discussion of the COs system In this section we will discuss the stability of the COs system before the impact of man, its cyclic nature, and mechanisms that control the pH and the distribution of CO2 species in the oceans. The composition of seawater has been assumed to have remained relatively stationary (time-invariant) for millions of years b y many workers (RUBEY [10], SILLEN [11, 12], HOLLAND[13], REVELLE and SUESS [14], BOLIN [15], SIEVER [16], HELGESONand MACKENZIE [17]) prior to the impact of man. This was based primarily upon the realization that the dissolved fiver load, if about the same through time, would have led to a much more concentrated seawater than the one we know, unless sedimentation removes salts from the oceans at approximately the input rate. This results from the short residence times of elements relative to the age of the oceans. Another line of arguments is based upon the unobserved effect of large excursions in seawater composition on the nature of marine sediments. Also, it has been suggested that large changes could have destroyed the continuity of life (WEYL [18]). This last argument may be a weak one because it is based upon the constancy of the pH which reflects the contancy of ratios of concentrations rather than of amounts of single components. There is an important although as yet unstated corrolary of the stationary ocean hypothesis which we ~ examine from the point of view of the COs system. It is that, if the outflows from reservoirs respond to their sizes, then any one reservoir can only remain stationary if all the reservoirs in the system are also stationary. In effect, if the size of a reservoir is increasing then the flux out of it increases and this perturbation is propagated throughout the system until a new stationary conditions is reached. This can best be seen in the mathematical models developed by PYTKOWICZ[5, 19]. It is likely that fluxes out of reservoirs respond to the reservoir sizes as, for example, the carbonate and silicate contents of rivers respond to the nature of the weathered continents [6], the air-sea exchange of COs depends upon the pCO~, and photosynthesis is enhanced by an increase in the COs concentration [2] even when this compound is not a limiting nutrient. T,he above argument is fairly evident for a system at a steady state (dynamic equilibrium) but may not seem as obvious if chemical equilibria control the composition of seawater. It is valid even then, however, because chemical equilibrium only controls the ratios of the forms of a given element unless the total concentration of the element is kept constant. This can readily be seen by the reaction A ~ B with K =

12

R. Pytkowicz

Hydrologie

(A)/(B). (A) and (B) are only fixed if (A) ~- (B) : constant; otherwise, the system can precess. If the size of the sedimentary reservoir or the atmospheric pCO2 change, the fluxes into the oceans and the oceanie TCO~ will also change and so will the concentrations of the individual CO2 species until a new steady state is reached. Thus, the stability of the CO2 system in the oceans is intimately related to that of the other CO~ reservoirs such as the sediments, the biota, and the atmosphere. It is likely that the composition of the oceans has remained relatively constant for quite a while and the stationary hypothesis will be accepted provisionally by us. Still, it is worthwhile to examine potential exceptions and uncertainties. It is not clear, for example, whether the sedimentary mass has remained constant or has increased with time E21]. Another problem is that of sodium which relates to the CO 2 system through Sillen's pH-stat mechanism Ell3. Calculations of the conversion of igneous into sedimentary rocks reveal an excess of sodium which winds up as NaC1 in the oceans and in pore waters E6]. If there is a net conversion of igneous rocks to sediments at present, that is, if these rocks do not simply belong to a sedimentary-metamorphic cycle, then it is conceivable that sodium is slowly accumulating in the oceans. If this is the case, then the pH-stat mechanism, which hinges upon the relationship K : (Na+)/(H+), is not effective in the long-term for which it was meant. We are not referring to weathering by CO2 in this instance but to weathering by HC1. If excess residual sodium were formed by CO2 weathering, this would imply that reverse weathering does not go to completion and would lead to a fast buildup of the alkalinity of seawater (see reaction (1)) as the bicarbonate concentration is much smaller than that of sodium. In the preceding paragraph mention was made of the possible cyclic nature of sedimentary processes. This will be a recurring theme throughout this discussion because cyclic processes enhance the probability of stability. Another point that was raised is that of reverse weathering, first proposed by GARRELS~11 to explain why the HCO~ produced in the weathering of Nalg and Llg by COs has not converted the oceans into soda lakes. Reverse weathering deserves further research because it is a necessary mechanism for oceanic stability and because it has not yet been demonstrated in its entirety in nature. Complete reverse weathering implies the conversion of clays into feldspars but, although aluminium-silicates can crystallize to clays, no authigenic feldspars have been found in the submarine sediments. Possibly, complete reverse weathering occurs in metamorphic environments E161 once SiO~ deposited by diatoms, sodium and potassium ionexchanged on clays, and alkalinity transported out of the oceans by the titration of clays are buried under the continents by seafloor spreading. The weathering of Calg (plagioclase feldspars) presents an even more intriguing question. It produces soluble Ca(HCO3)2 which at present can be removed from the oceans by organisms as insoluble CaCO3. This sequence of reactions probably produced much of the sedimentary carbonates although, before the advent of calcareous organisms, the precipitation could haye occurred inorganically in shallow seas (inorganic precipitation in the open oceans with the present Mg/Ca ratio of seawater is not feasible ~2]. The question that concerns us is whether or not new sedimentary carbonate rocks are being formed by the biogenic precipitation of carbonate resulting from the weathering of Calg. If this is the case and the CO2 system is cyclic, then the sedimentary reservoir within the cycle is increasing and, by the argument presented

35/1, 1973

Carbon Dioxide System in Oceans

13

earlier, the oceanic C02 cannot be stationary. If it is indeed stationary, one must assume that the C02 in the CaC03 which results from the weathering of Calg belongs to a subcycle (1-2-3-D-7-H-9-K-M-1 in Fig. 1) and that the CaC03 is metamorphosed back to Calg at M. The response of fluxes to reservoir sizes can be justified not only on the basis of enhanced chemical denudation from continents that contain larger amounts of the element in question but also because normally the rates of reactions increase monotonically from zero in the absence of reactants to successively larger values as the amounts of reactants are raised. The preceding arguments do not b y any means destroy the stationary hypothesis but simply point out that further work is needed before the hypothesis can be completely verified. In the next section, we will accept the stationary ocean in order to facilitate our calculations, with the realization that slight trends and fluctuations should not invalidate our rough results. First though, we will seek mechanisms that can account for the rough invariance of the C02 system before the advent of large-scale fossil fuel burning. We must, as a first step, account for the constancy of the atmospheric pC02 if truly juvenile COs, which results from the degassing of new mantle material rather than from the oxidation and metamorphism of sediments, is being injected into the atmosphere. We cannot, as was done by earlier workers, conclude that the ocean has acted as an ultimate sink because, if this were the case, the COs system in the oceans would not have been stationary. The weathering of sedimentary carbonates does not permanently consume juvenile COs because this COs is released when calcareous organisms transform Ca(HCO3)~ into biogenic CaCOv Also, reverse weathering of clays compensates for the COs used up in the weathering of potassium and sodium feldspars. One possible sink for the removal of juvenile COs, which is compatible with a stationary atmosphere and ocean, is the permanent withdrawal of refractory org-C into sink 11. Another one is sink 10 which could accumulate some of the CaC08 formed by the biogenic uptake of Ca(HC03)2 released during the weathering of plagioclase feldspars. The carbon in this CaCO3 is of atmospheric origin. These are the reasons why the model in Figure 1, although primarily cyclic, has an open input and outputs. Still, one could conceive an extreme case in which there is no truly juvenile C03 and in which sinks 10 and 11 are coupled to the atmosphere. Next, we will examine the intriguing stability of the seawater pH. Such a stability is indicated, for example, by the continuity of life [18], by the absence of mineral phases such as brucite in the submarine sediments, and by the lack of evidence for drastic changes in the atmospheric pCO~ in the past with the exception, of course, of the primaeval ocean. The classical view held since the work of BUCH et al. [22] was that the pH was buffered by the CO, system present in seawater. SILLEN [11] suggested that the true long-term buffering of seawater was actually a pH-stat mechanism maintained by aluminium silicates. PYTI~OWlCZ[3] showed that the alkalinity alre~dy present in the oceans can buffer the pH for periods of at least a few thousand years even if reverse weathering is neglected and for much longer periods when reverse weathering is taken into account. Thus, he showed that the two mechanisms could coexist. Actually, there are three problems related to the oceanic pH: the long term

14

R. Pytkowicz

Hydrologie

pH-stating or buffering that counteracts the injection of acid volatiles, the shortterm buffering capacity that moderates pCOs and (CO~-) changes resulting from thermal and biological effects, and the actual pH which occurs within the buffer range of seawater. Sillen was concerned with the first problem and felt that the C02 system cannot cope with the injection of acid volatiles and that pH-stating was achieved by the utilization of these acids in the titration of aluminium silicates. His pH-stating is a possible mechanism but, in addition, the removal of COs into sedimentary sinks 10 and 11 by biological processes can contribute to the control of the pH [5]. There is a weakness in Sillen's proposal because his reaction, which leads to the condition (Na+)/(H +) = K , presupposes that (Na +) remains constant. Thus, he assumed a stationary ocean to obtain a stationary pH. Also, the equilibrium constant K and the activity coefficients of (Na +) and of clays, which are charged particles and do not have unit activity, are not known at the temperatures, salinities, and pressures which are encountered in the oceans. Another difficulty is that the COS taken up in the titration of Nalg and Klg is released in reverse weathering so that this iitration alone cannot prevent a buildup of juvenile COs in the atmosphere and in the oceans. For these reasons I tend to favor the biological sinks, namely, the removal of biogenic CaC08 resulting from the weathering of Calg and of org-C, as the agents that counteract the effect of juvenile COs on the long-term oceanic pH. Sillen's mechanism can account for other acid volatiles such as HC1. For short-term processes within the oceans such as photosynthesis, oxidation, solution and precipitation of carbonate, changes in the temperature of seawater, and evaporation the buffer capacity is supplied by the COs system through the alkalinity (essentially HCO~ already present in seawater [3]). Roughly 88% of this alkalinity results from the weathering of sedimentary carbonates and the remaining from the weathering of igneous rocks [5]. The actual pH within this buffer range is fixed by any two relevant quantities such as the pCOs and the alkalinity of seawater E4]. The pCOs below the thin wind-mixed layer is not at equilibrium with the atmosphere but is regulated by the rate of oxidation of organic matter while the alkalinity is in large measure the result of a balance between the input of weathered products and the biogenic removal in settling tests. Of course, purely chemical considerations such as the effects of pressure, temperature, salinity and ion association upon the dissociation constants of carbonic acid [23, 14], the redissolution of calcareous tests [3, 25], and thermal processes also play a role. It is interesting to observe, though, that organisms play an important role in maintaining the pH at values within which they can survive. Thus, we saw that, although the stationary hypothesis for the chemical composition of the oceans is not completely established, once it is accepted a coupling of weathering and biological processes can be used to explain the stability of the atmosphere and of the oceanic pH. It was also shown that the constancy of part of the COs system implies the constancy of the whole system. This leads us to a very iliteresting question which will be examined next because constancy implies a stability mechanism in operation. A stationary ocean may result either from chemical equilibria or from steady states (dynamic equilibria). These alternatives were discussed briefly by PYTI
35/1, 1973

Carbon Dioxide System in Oceans

15

standing of the control of the oceanic composition. The mechanical analogues of equilibria and steady states are a ball at the bottom of a potential well and the constant level of a reservoir through which water is flowing. Chemical equilibria only fix the concentrations of given forms of an element if there are enough conditions to use up all the degrees of freedom; normally they only determine ratios of activities or concentrations. In a chemical reaction X ~- Y ~ Z there is chemical equilibrium when the rates of the forward reactions are equal to the rates of the reverse reactions. There is a steady state of Y if there are net reactions X -~ Y and Y -~ Z but the rates of production and removal of Y are equal. Thus, steady states are less restrictive than equilibria. Closed chemical systems such as reactions in closed containers eventually reach chemical equilibrium and colour the views of laboratory chemists who undertake the study of natural open systems. In open systems one may find energy and matter fluxes, which correspond to gradients of energy and chemical potential and which are the domain of irreversible rather than equilibrium thermodynamics. A typical example is the lack of oxygen equilibration at the sea surface in summer [26,27]. SILLEN [ 11,12] suggested an equilibrium model as an approximation to explain the chemical stability of the oceans, from the point of view of elemental ratios rather than individual concentrations. He proposed that the chemical species dissolved in seawater may be nearly at equilibrium with the aluminium silicates which are brought by rivers and which settle through the oceans. This hypothesis has been expanded upon and supported by several other workers (e.g., HOLLAND [13], BOLIN [15], SIEVER [16], HELGESON and ]~LkCKENZlE [17]).The model of Sillenis an important contribution because, as a tendency towards equilibrium drives most natural systems, equilibrium controls the direction of chemical reactions and m a y perhaps have been nearly achieved for some of the seawater solutes. Of course the biota can work in the opposite directions as in the case of benthic foraminifera removing calcium carbonate from undersaturated waters. Equilibria between dissolved salts and mineral phases have not, however, been proven to exist in seawater. Equilibrium constants for the desired reactions are not known well enough as functions of temperature and pressure to test the model with confidence. The total or stoichiometric activity coefficients [28], needed to translate thermodynamic constants into equilibrium concentrations, depend not only upon the ionic strength, temperature, and pressure but also upon the poorly known extent of ion association [29]. The activity coefficients of clays, which are charged particles, are assumed to be i as for nonelectrolytes. The effects of organic and inorganic coatings upon the kinetics of equilibration of mineral grains [2, 30, 31, 32, 33] require further study. It is possible that major ions may reach equilibrium with aluminium silicates but trace metals may be kept from equilibrium if they react significantly with the biota and with dissolved and particulate organiG matter. Nutrient concentrations appear to b4 regulated by life rather than by mineral interactions [34]. In two well documented cases, CaCO~ [27, 35] and Si02 [36], the dissolved phases are not at equilibrium with the solids. In the case of CaCOs the near-surface waters are roughly 200-400% saturated while deep waters may only be 50~/o saturated. If equilibrium exists between major ions and clays, one may wonder why the oceanic distribution of these

16

R. Pytkowicz

Hydrologie

ions does not reflect in the nature of the suspended and settled clays. Perhaps hydrodynamic factors such as turbulent mixing are faster than ionclay equilibration. WEYL [18] and BROECKER [37] suggested, as an alternative to equilibrium, that the oceans are at a steady state, that is, that their chemical composition is kinetically controlled. PYTKOWlCZ[5, 19] deduced the general conditions that lead to an equilibrinm versus a steady state ocean and showed that one or the other may be the controlling condition for different chemicals. The models are presented in the appendix in a more complete manner than was done earlier, for greater clarity. Linear models were used without loss of generality, as the conclusions apply to any models in which fluxes respond to reservoir sizes. The main results, which will be applied to the C02 system, are: 1. A steady state ocean will occur for chemical systems for which the size of the weathering reservoir on land is not seriously depleted within the time scale of interest, independently of whether the systems are controlled by biological or by .mineral equilibration processes. The constancy of the land reservoir can result from a small outflux, uplift of new material, or cyclic replacement. 2. Biological processes or non-specific interactions with particulate matter lead to a steady state ocean even if the land reservoir is depleted. 3. Sillen's equilibrium ocean occurs if depletion of the continental reservoir is coupled with removal of species from seawater by mineral-seawater processes that can be characterized by an eventual equilibrium. With regard to the C02 system, it is to a large measure subjet to cyclic replacement, the removal of alkalinity from the ocean is primarily biogenic [2], the dissolved carbonate is not at equilibrium with CaC03 as near-surface seawater is two- to fourfold supersaturated while, primarily because of pressure, deep waters are quite undersaturated [35, 38, 39, 40, 41, 42] and the pCO`, below the thin wind-mixed layer is primarily controlled by oxidation (see, for example, the distribution of pCO`, with depth in CULBERSO~ and PYTKOWlCZ [23]. Thus, according to the conclusions presented above, the CO`, system, if stationary before the impact of man, is at a steady state rather than being controlled by equilibrium reactions. Of course, seawater-mineral equilibration enters in a secondary, although important manner, in the dissolution of calcareous tests at depth. The undersaturated deep oceanic waters dissolve over half of the settling tests and the recycling of the dissolved material b y upwelling enhances the alkalinity of seawater and, therefore, its capacity to buffer the pH and changes in the atmospheric C02. Still, this refers to processes within the oceans rather than to the mechanism for transport through them. The atmospheric C02 also is in a steady state as the eventual removal of juvenile CO`, through the oceans and to the sediments is achieved by biological processes. The near-equilibrium of the atmosphere and the surface seawater cannot be claimed as a control mechanism for the atmospheric CO., because all it can produce is an attenuation of changes through the partition of the gas between air and water rather than a complete removal of juvenile material. The rates of weathering are controlled by the runoff of ground waters and by their CO`, load, which results from oxidation on land, and thus are in a dynamic rather than an equilibrium condition. Of course, saturation of ground waters with

35/1, 1973

Carbon Dioxide System in Oceans

17

CaCO 3 can limit weathering but this is a secondary process as it can be overcome by an enhanced flow or a larger p C O s. Life at sea is not a respecter of mineral-seawater equilibria as can be seen by the utilization of CaCO 8 by benthic foraminifera in deep undersaturated waters and by diatoms in waters that are undersaturated with respect to amorphous silica.Thus, it seems plansible that the COs system, if stationary before the enhancement of fossilfuel burning, was at a steady state in which the size of the various reservoirs grew; this was followed by an increase in weathering, gas exchange across boundaries, and biological utilization,until exit rates became equal to input rates. The question of whether the CO2 system is completely cyclic or is open-ended was examined in the preceding discussion but no definite answer was obtained. Still,it appears to be primarily of a cyclic nature as it is composed of a large number of loops. This is important from the standpoint of perturbations because it implies that they are not dissipated in an ultimate reservoir but tend to distribute themselves through the various reservoirs and remain with us. Although steady state systems respond to changes in fluxes or in the total amount of the component present in the overall system, they have a stating capacity because of the attenuation induced by the redistribution of perturbations [191. This capacity will become evident when the long-term effects of fossilfuel burning are discussed in the last section. It is worthwile to point out that, in a cyclic system, the time behavior of any given reservoir size X~ during a transient period is not simply related to the relaxation time X~/J~:l,where jr~jis the flux out of i, but that it responds to a linear combination of all the relaxation times for the system. Thus, all the relaxation or storage times must be taken into consideration in reservoir kinetics unless some of them are much longer than the time scale of interest ES]. There is a troublesome question regarding the cyclic nature of carbonates, because it is difficultto visualize the carbonates which are produced by the weathering of limestones and dolomites and which settlein deep oceanic waters as being returned to the continents in the form of sedimentary carbonate rocks. They eventually reach metamorphic environments and should be uplifted as marble or Calg. Thus, deep carbonates would be returned as metamorphic products while shallow ones would yield sedimentary rocks. This would not necessarily invalidate a stationary ocean because it is conceivable that the depletion of CaCO3 and the formation of Calg at depth could be compensated by the formation of new C a C O 3 from Calg in shallow environments by the process described earlier, namely, the weathering of Calg to Ca(HCOs) s and the biogenic conversion of Ca(HCO3)~ to C a C O 3. To conclude this discussion, mention will be made of a property of seawater which was implicit in the preceding material and which gives it the capacity to buffer short-term changes in p H and in atmospheric pCOs. This is the large TCOs content of seawater, roughly sixty times as much as in the atmosphere and which is present primarily as carbonate alkalinity, CA=(HC-O~) % 2(CO~-). The large alkalinity is due to t~o factors: the high solubility of CaCO8 in seawater which is two orders of magnitude larger than that in distilledwater, and the recycling of carbonates within the oceans. The enhanced sohibi]_ityis due in part to the ionic strength of seawater and also to ionic interactions between cations and carbonate E24, 43~. It is interesting to observe that a rather microscopic phenomenon such as ionpair formation, which

18

R. Pytkowicz

Hydrologie

usually does not concern earth historians, is a crucial factor in preserving the oceans as we know them. In summary, the COs before the advent of man may have been roughly stationary and is in great measure cyclic. The regulating mechanisms for the atmospheric C02, for the pH buffering of seawater, and for the distribution of CO, in the oceans results from a complex of weathering, biological, hydrographic, and purely chemicalprocesses rather than from a simple set of mineral-seawater equilibria. Much is known about carbon dioxide in nature but, when one attempts to understand the system as a whole b y a weaving of established facts and surmise, gaps in our knowledge point out to needed research. This will become even clearer in the next section, in which rough estimates are presented of the fluxes and reservoir sizes which are useful for studies of the effect of fossil fuel burning upon the COs system.

A quantitative model of the C02 system A numerical model, corresponding to the block diagram in Figure 1, will be obtained in this section. The tedious calculations which are required can be bypassed by readers who are solely concerned with the main thoughts presented in this work. The quantitative model is presented in Figure 2. The reservoir sizes are in 10 2o gC (grams of carbon) and the fluxes in 101. gC/yr. The number of significant figures is well in excess of the accuracy of the data but is needed for mass balance computations. The uncertainties in the data were presented in an earlier model of PYTKOWICZ [3] but are not reproduced here to maintain the diagram as simple as possible. A stationary ocean and a residence time for deep oceanic waters of 1,000 years were accepted in the calculations. The sizes of reservoirs 1, 2, 5, 6, 7, and 8 were obtained from the compilation by REVELLE and FAIRBRIDGE [44]. The size of reservoir 3 was estimated from the average pCO, of ground waters [6], the volume of ground waters [45] which is roughly 1/i0 of that of the oceans, and the solubility of COs in seawater [46]. A very rough idea of the size of reservoir 9 was obtained by assuming that only the upper 10 cm of the submarine sediments are in exchange contact with seawater and by using the average CaCO 3 content of the sediments from SVERDRUP et al. [47]. Estimates of the amount of carbonate present in tests in the water column were not available. The flux of juvenile COs is 0.082 • 101. gC/yr [48] and Ji~n+JK.xo=o.082 • 1014 gC]yr. JL-n and Jx-10 were taken as proportional to the values of Js-L and Jvz, which will be calculated later. These three fluxes are small compared to the cyclic ones and the apportionment of juvenile CO2 through the system is cumbersome and would detract from the clarity of what follows. For these reasons, J(juvenile COs), JK-lo and JL-n are shown in parentheses and are not included in the mass balance computations. " Js_~.=2.460x101. gC/yr [5, 48, 49]. J ~ . . 7 = 2 x J s - E = 4 . 9 2 0 x 1 0 1 . gC/yr (see reaction 2). This is twice the value from CLARK~-[45] since his data were obtained from inicinerated river bicarbonate samples with a consequent loss of half of the C0v Also from reaction 2, Js-~. = Js-x- Jvl~-9 =0.200 x l 0 1 . gC/yr [8]. JJ-s =Js-~. + J v g = 2.660 x 101. gC/yr according to the stationary hypothesis.

35/1, 1973

19

Carbon Dioxide System in Oceans

J3.D=JD.~=0.682• gC/yr [5, 48, 49]. Part of JD-~, TCCa) JD-?, results from the weathering of Calg. The carbon in the C02 used in this weathering follows paths 1-A-2-B-3-D-7-H-9-J-K-M-1 and 1-A-2-B-3-D-7-H-7-1, that is, half of the COs is returned to the atmosphere during the biogenic conversion of Ca(HCO3)s'to CaCOs and the other half is returned following metamorphism of CaCO a to Calg at M. JD-? T(ca) was calculated from JD-v and the average composition of igneous rocks presented by GARRELS and MACKENZIE [6] and was found to be 0.382 • 101. gC/yr. Half of this flux appears as CaCO 3 at H and the rest, as COs, returns to reservoir 7. Thus, Jx-M-z= 0 95 vA JD-7 T(C~l = 0.191 • 10z* gC/yr. Jg-I, the rate at which tests dissolve, is 3.79 • 10z* gC/yr [3], and Jo-I, the rate at which COs is utilized in the dissolution, is also 3.79 • 10z* gC/yr, as can be seen from reaction (2). The returning flux of COs in the form of HCO; to reservoir 7 is JI-~ = Js-I Js-I. J~r-7, the rate of utilization of HCO~ by tests, is Ji-~ + J~.-~+ JCDC-~=12.882 • 10~4 gC/yr. Thus, tests utilize bicarbonate brought by rivers plus that recycled from deep waters. Half of this bicarbonate becomes test carbonate and half becomes COs. Thus, J~-9 = J;r.~ = 6.441 x I0 I* gC/yr.

[ATMOSPHEREI

(0.082)

650.00__0~654.151

199.000

194.658

'~A 197., = 197.8

-

~

L500

1,260.0 0~.~ L ~ ~' F = J 74~1,261.2 r G 2..57.4/

0.682

7.

4.920

__21_ _ ___j__ j

, ~,. o

4. ~

e 2.460

/,-16.-I 0.20~

!-

).300 2.851

2.660 0.191

(0.008)

10.074)

I-

o oo

Fig. 2. A quantitative model of the CO2 system. The reservoir razes are in 108~ g C and the fluxes in 1014 g C/yr.

20

R. Pytkowicz

Hydrologie

Next, we will examine the org-C cycle. I found no information on J~_~, the rate of lithification of org-C on land, and Je-c, the subsequent rate of physical weathering of the lithified org-C. Js-L-6, the flux of org-C into submarine rocks, and Js-B, the flux of chemical weathering of this org-C by oxidation, are 0.3 • 1014 gC/yr [8]. J1-A-,, the gross rate of photosynthesis on land, is 199 • gC/yr [48] and 1.5 • 1014 gC/yr of the resulting org-C are transported to the oceans as dissolved and particulate organics [8]. J~-B is J1-A-~-Jve-s=197.5 x 101~ gC/yr. JB-s is J~.~+J..~= 197.8 X 1014 gC/yr. J3-1=JB-a- (J3-D +Ja-E) =194.658 x 1014 gC/yr. Thus, there is a net uptake of COs by land and, as ~ be seen later, there is a net release of COs by the oceans. It is difficult to obtain this net release from pressure heads across the sea surface, as these pressure differentials are masked by seasonal and geographical variations which are strong enough to cause spacial and temporal reversals in the local directions of the net gas fluxes. J~-e-s, the rate of gross photosynthesis in the oceans, is 1,260X1014 gC/yr [50]. Js-G, the rate of oxidation, is JT-v-s + J v c - s - Ja-L = 1,261.2 • 1014gC/yr as, according to GAm~ELS and MACKENZIE [8], Js-T,=0.3 x l014 gO/yr. PYTKOWlCZ [4] estimated from the oxygen utilization that org-C equivalent to 23.8 • 1014 gC/yr is oxidized in deep oceanic waters. Thus, 9 8 . 1 ~ of the oxidation of org-C in seawater occurs in the near-surface layers. JG-~ = J s - G - JG-I = 1,257.41 • 1014 gC/yr. Jl-~ = 650 • 1014 gC/yr [51]. JT-I is the balance between the inputs and outputs of reservoir 7 and is 654.151 • 1014 gC/yr. Again, it should be emphasized that the number of significant figures used in this work is that required for mass balance and does not represent how well the fluxes are known. The quantitative model which was obtained in this section will be of use for estimates of the long-term effects of fossil fuel burning upon the COs system in nature, once the actual rate laws which control the fluxes between reservoirs are determined [5].

Summary 1. A qualitative description of the C02 system in nature was obtained b y means of a model containing 11 reservoirs with 30 fluxes. This block diagram, which is more complete than earlier ones, was helpful for a discussion of the mechanisms that control the COs system and for the estimate of the long-term impact of fossil fuel burning. 2. The control mechanisms for the COs system were examined. It was found that the system probably was roughly stationary before the impact of man although questions such as the effect of excess NaC1 produced during weathering on the pH-stat mechanism and of the weathering of plagioclase feldspars on the size of the sedimentary carbonate reservoir remain to be answered. The constancy of the system implies a'stabilization mechanism and it was concluded that this mechanism is primarily a steady state rather the result of chemical equilibria. The distribution of CO s components in the oceans and the stability of the pH of seawater were found to result from a complex of weathering, biogenic, and purely chemical processes rather than from simple mineral-seawater equilibration reactions, with biological removal of CO s from

35/1, 1973

Carbon Dioxide System in Oceans

21

the oceans as org-C and CaCO, playing an important role in the atmospheric and seawater stabilities. ZUSAMMENFASSUNG 1. Das nati~rliche COa-System wurde mit einem Modell beschrieben, welches aus 11 Reservoiren und 30 Querverbindungen besteht. Dieses Blockschema, vollstAndiger als frilhere, client als Grundlage zur Diskussion yon Mechanismen, welche das C O f S y s t e m kontroUieren, sowie fllr eine Beurteilung der Einfll~sse, die durch die Verbrennung fossiler Brennstoffe entstehen. 2. Die Kontrollmechanismen des COl-Systems warden untersucht. Man land, dass vor der Eiuwirkung der menschlichen Zivilisation das System wahrscheinlich ann~ihernd stationgr war. Unter anderem bleiben folgende Fragcn unbeantwortet: Welche Auswirkungen hat Oberschl~ssiges, bei der Verwitterung entstehendes NaC1 auf das p H - S t a t - S y s t e m ? Wie beeinflusst die Verwitterung des Plagioklas (Feldspat) das Karbonatreservoir im Sediment ? Aus der Konstanz des Systems wird auf einen Stabilisationsmechanismus geschlossen; diese ZeitunabhAngigkeit beruht vor allem auf der EinsteUung eines komplizierten Steady State (Fliessgleichgewichts) und weniger auf Grund chemischer Gleichgewichte. Die Verteilung der COa-Komponenten und die Konstanz des p H des Mcerwassers ist die Folge der stationAren Wechselwirkung zwischen komplexen Verwitterungsreaktionen mit biogenen und rein chemischen Prozessen und ist nicht auf einfache thermodynamische Gleichgewichte zurOckzu1~hren. Die biogene Transformation yon marinem CO~ in organischen Kohlenstoff und CaCO~ spielt eine besonders wichtige l~olle bei der Regulierung und Konstanthaltung des Gehaltes an CO~ in Atmosphi~re und Ozeanen.

m~suMr 1. Le syst~me naturel du CO 2 a ~t6 repr6sent~ par un module comprenant 11 r6servoirs et 30 liaisons transversales. Ce schema en bloc, jusqu'ici le plus complet, sert de base pour la discussion des m*chanismes qui r~gissent le syst~me COl et pour 6valuer les influences proven~nt de la combustion des carburants fossiles. 2. Les m~chauismes de contrSle du syst~me CO 2 ont 6t6 examin6s. I1 a *t~ constat6 que le syst~me a probablement ~t~ stationnaire avant l'influence de l'homme moderne. Cependant les questions suivantes demandent encore une explication: Quels sent les effets du NaC1 en exc~s caus~ par l'~rosion sur le syst~me pH-stat ? Quels sont les effets de l'~rosion des plagioclases (feldspath) sur le r~servoir du carbonate dans le s6diment ? La constance du syst~me laisse conclure qu'il y a un m~chanisme stabilisant; ce syst~me, ind6pendant du facteur temps, est surtout bas6 sur l'&ablissement d'un ~steady state, (~quilibre dynamique) et non sur un 6quilibre chimique. La distribution des diff6rentes formes du CO 2 et la constance du facteur p H de l'eau de mer r~sultent de l'interaction stationnaire entre des r6actions 6rosives complexes et des processus biog~nes et purement chimiques; elles ne peuvent pas ~tre attribu6es ~ de simples ~quilibres thermodynamiques. La transformation biog~ne du CO2 de l'oc6an en carbone organique et CaCO a joue un rSle particuli~rement important dans le r6glage et la constance du CO2 dans l'atmosph~re et les oe6ans.

Appendix General conditions for equilibria versus steady states The general conditions for an equilibrium or for a steady state ocean will be derived and it will be shown that SILLEN'S [11] model is just one of several possibilities. The models will be kept as simple as possible not to obscure basic principles by mathematical formalism. Only three reservoirs will be considered: a) which is the weathering reservoir on land, b) the oceanic one and c) the submarine sediments. The amounts of a given element in the reservoirs will be expressed by A, B,. and C.

22

R. Pytkowicz

Hydrologie

The rate laws which govern fluxes out of reservoirs are probably quite complex and, in general, are not known. They m a y be nonlinear as, for example, in the weathering of carbonates which should involve the product of a carbonate and a CO2 term. This weathering depends upon the rate of photosynthesis on land followed b y the decay of organic matter, with production of CO2 which enters the ground waters and weathers carbonates. Thus, there are several steps in the process and the form of the law will have to be established experimentally. These considerations can be bypassed in our conceptual approach. In effect, if a reservoir such as the continents does not contain a given chemical, then the weathering rate is zero. This rate should increase with an increasing amount of the chemical. The simplest way to express this behavior is to assume that the weathering rate and, therefore, the flux into the oceans, is proportional to the reservoir content. The general conclusions from the model will be valid because they apply to any system in which outfluxes increase monotonically with the reservoir contents. Such an increase is indeed observed for the response of the biota to the pC02 [20], the rate of weathering as a function of the geological nature of continents [6], and the exchange of gases across air-water interfaces. The simplest models will be treated first and we will start with the following one: Model 1 dA

d~--

dB dt

kAa

= kaA-kBB

dC dt

= kBB.

(1) (2) (3)

This model reflects exit rates which are simply proportional to the amounts of an element which are present in the reservoirs. No equilibrium condition within reservoirs was imposed upon the model and, therefore, removal of B from seawater in this case cannot be by mineral-seawater equilibration. This model represents removal by nonspecific processes such as biological uptake and physical adsorption. Of course, biological processes m a y involve chemical equilibria but these equilibria occur in body fluids rather than in seawater. The model is an open chain one; cyclic processes will be treated later. I t does not imply that concentrated ions will necessarily be removed from the oceans faster than dilute ones as the rate constants for different ions m a y not be the same. The solutions of (1) and (2), with the initial conditions A ~ A o and B = 0 at t = 0, are

B=

A =. Aoe-~A* ha A o k B - k a (e-~at-e-~Ist)"

(4) (5)

A is gradually depleted while B, the oceanic content of the given element, will increase to a m a x i m u m value and will then gradually decrease to zero. Eventually all of

35/1, 1973

Carbon Dioxide System in Oceans

23

A 0, the amount initially present in the weathering environment, will be present as Coo in the submarine sediments. This model does not yield a non-zero stationary state for B.There may, however, be an apparent steady state in the region around the m a x i m u m value of B as this region m a y last millions of years.

Model 2 This model is a special case of model 1 in which it will be assumed that A = A o is essentially constant because of its size or of replenishment. This replenishment m a y be due to simple uplift or m a y result from the cycling of submarine sediments, a process examined for example by GARRELS and MACKENZIE [6]. Then, the solution of (2), with the initial condition B = 0 when t = 0, is B = A0~

ka

( 1 - e -kBt) .

(6)

(6) tends towards the steady state B ----Aoka/kB, which makes dB/dt = 0 in (2). This is an interesting result because it implies that the oceans will reach a steady state if two conditions which m a y be reasonable are satisfied: that the rates of removal increase with increasing amounts of reactants in the oceans and that the amounts in the continental weathering reservoir are not seriously depleted either because of the reservoir size or because of replenishment. This model corresponds to an ocean in which the amounts of solutes gradually increase. This increase causes a corresponding increase in the exit rates until eventually the exit and entry rates become equal and a steady state is reached. The steady state system has some stability to perturbations because if B for example should increase then the flux from B to C, kBB, would increase and would counteract at least in part the increase in B. As an example, if the amount of dissolved calcium carbonate in the oceans should increase then two factors would tend to enhance the rate of removal of calcium carbonate from seawater. The rate of production of calcareous organisms could increase and the rate of dissolution of settling or settled calcareous tests would decrease because the deep oceans would be less undersaturated. Thus, more calcareous tests would be incorporated into the sediments. This example goes beyond the scope of equation (6) because it touches upon the effect of intra-reservoir equilibration when the degree of undersaturation is considered. The treatment of cases in which there m a y be equilibration within reservoirs will be treated next.

Model 3 The possibility of equilibration within reservoirs will be included in this model. Thus, this model represents SIr.LE~'s [11, 12] hypothesis. I t can easily be shown that the simplest formal representation of mineral-seawater equilibration within the oceans is dA -- -kAA dt dB kaA-ks (B-B*), (7) dt -

-

R. l:~kowicz

24

Hydrotogie

where B e is the amount of the element when at equilibrium with minerals. Amounts are used rather than concentrations so that the reservoir kinetics can be extended to solid reservoirs. This presents no conceptual difficulty because the constant reservoir volumes which would appear if concentration units were used are simplyincorporated into the rate constants. The solution of (8), with the initial conditions A = A 0 and B = 0 when t = 0, is B = B*

ka (1--e - ~ t ) + A o k B - k a ( e - ~ a ~ - e - ~ B 0

(9)

and the system tends towards the equilibrium condition A = 0, B = B*, and C = Ao-B*. In this model B is initially zero and both terms in (8) are positive which means that B is added to the oceans as dissolved ions in rivers and from the solid phase also brought b y rivers. B can exceed B* because of the dissolved river flux until k,lA = k B ( B - B*) and from this point on the uptake b y solids (possibly clays) exceeds the dissolved input kaA, as A is being depleted. This leads to a decrease in B until the equilibrium value B e is eventually reached. At this time kaA has become negligible. Thus, this is an idealized model t h a t represents the time behavior of an ocean whose cation concentrations tend towards equilibration with aluminium silicates. I t can be seen that mineral-seawater equilibration in conjunction with depletion of the continental reservoir leads to a Sillen ocean. Model 4 In this model, the counterpart of 2 and a special case of 3, A will be assumed to be essentially constant. I t ~ be shown that, as a consequence of A = A 0, the constant influx from reservoir a m a y prevent equilibration and lead to a steady state in the oceans. The solution of (8), with A = A o and the initial condition B = 0 at t = 0, is B =

Be

( 1 - - e - ~ s 0 + Ao ~

ka

(1-e-~B0-

(10)

B tends towards B = B e + Aoka/kB for which dB/dt in (8) is zero. B will only tend towards its equilibrium value Be if Aoka/kB is negligible relative to B e, t h a t is, if the rate constant for the dissolved river input is very small compared to the rate constant for the uptake b y clays. Next, cyclic systems Hill be examined because m a n y chemical constituents of seawater probably cycle from the continents to the oceans and then back to the continents via the submarine sediments. Model 5 (cyclic) " A three reservoir model will be used for simplicity. The system will be considered cyclic, with A going to B to C and then back to A. The differential equations are dA --. dt

= k v C - kaA

(11)

35/1, 1973

Carbon Dioxide System in Oceans dB dt

25

= kAA - k~B

dC d.r -- k s B -

(12) (13)

kcC .

The open chain models are special cases of 5 for negligible values of kc. The cyclic counterparts of models 3 and 4 will not be treated in detail as model 5 is sufficient to illustrate the desired concepts. Cyclic systems are of special interest because they often occur in nature. The carbon dioxide system, in addition to its broad cycle from the continents to the oceans and back to the continents, undergoes several sub-cycles within the oceans and to the atmosphere, as was shown in the text. Nutrients such as phosphate and nitrate are cycled through the biosphere and the oceans. Silicate minerals are weathered on the continents and the resulting aluminium silicates which are brought to the oceans undergo eventual reconstitution to silicates [1, 16]. The first question that arises from equations (11) through (13) is whether such a system tends towards a stationary value or if it can diverge or oscillate. I t was shown b y Professor M. S. Longuet-Higgins (personal communication) that the system does indeed tend towards a stationary condition even if the roots are complex. The general solution of equations (11) through (13) is of the type A =

C x oc x + C~ or 2 e~ 2~ + C~ or 3 e~ 3t

(14)

B = Caflx + C,fl2ev2~ + C~83e~

(15)

C = Cxyie~ u + C~y~e~ 2~ + C3yne~3t.

(16)

If the system starts from some non-stationary state then, as time goes on, the terms in p , and P3 will vanish and a steady state of the type A = Cxax, B = Cx/~a, and C = Cxyx will be reached. The general case of n reservoirs in which each m a y interact with the other n-1 reservoirs and which m a y or m a y not be cyclic, with or without internal equilibria, can easily be shown to yield solutions of the type X , = X~ + C x 0r ,xe~ xt + ... + C,, + inelont .

(17)

The steady state solution for equations (11) through (13) is A-

T kar'B--

T k,~r'and

C--

T kcr

(18i

with T = A + B + C and r = 1/ka + l / k s + like. These equations show that the steady state amount in any one reservoir is a function of the total amount and of the rate constants (the reciprocals of the relaxation times) for all the reservoirs. Therefore, it is not possible as has been attempted b y some to explain the stationary state in any one reservoir b y processes within that reservoir alone it but is necessary to consider the 6thole system. Two types of perturbations are possible. Firstly, T m a y change in which case A, B, and C will gradually approach new values which will still maintain the proportionality A : B: C: :l/kA :1~ks : l / k c . (19)

26

R. Pytkowicz

Hydrologie

Secondly, a rate constant, for instance ha, m a y change to a new value k~/. In this case the new values of A, B, and C will be A ' = A kA/kAr; ' B ' = B r / r ' , a n d C' = Cr/r'. The system is not buffered in the usual sense but B and C does not change in proportion to the change in ka because 1/ka is only one of the terms in r. I t can also be easily shown that a given change o f / ~ into a large reservoir will have a larger effect upon the reservoir sizes than the same change in a small one. This occurs because large reservoirs at a steady state have relatively small values of k and, therefore, 1/k, becomes an important term in r. In conclusion, it was seen that an equilibrium ocean will occur if the land reservoir of a given element is reasonably constant and if mineral-seawater equilibration reactions control the removal of the element from seawater. If the land reservoir is depleted then equilibrium m a y be approached only if the rate constant for weathering is slight. Cyclic systems were shown to tend towards stationary values and to have a capacity to resist in part the effect of perturbations. ACKNOWLEDGMENTS

This work was supported b y the National Science Foundation G r a n t GA-17011 and b y the Office of Naval Research Contract N00014-67-A-0369-0007. I t was started while the senior author was a National Science Foundation Senior Postdoctoral Fellow at the D e p a r t m e n t of Applied Mathematics and Theoretical Physics at the University of Cambridge and was completed at the Bermuda Biological Station. He gratefully acknowledges discussions with Professor M. LonguetHiggins and access to the manuscripts of books b y Professors R. M. Garrels and F. T. Mackenzie. REFERENCES

[1] GAEEELS, R. M., Silica: Role in the Buffering of Natural Waters, Science 7d8, 69 (1965). [2] PYTKOWiCZ, R. M., Rates of Inorganic Calcium Carbonate Nucleation, J. Geol. 73, 196-199 (1965). [3] PYTKOWICZ, R. M., Carbonate Cycle and the Buffer i~Iechanism of Recent Oceans, Geochim. Cosmochim. Acta 37, 63-73 (1967). [4] PYTKOWICZ, R. M., Carbon Dioxide-Carbonate System at High Pressures in the Oceans, in: Oceanogr. Mar. Biol. Ann. Rev. 6 (Ed. H. Barnes; George Allen and U n w i n Ltd., London 1968), p. 83-135. [5] PYTKOWlCZ, R. M., The Chemical Stability of the Ocean* and the CO 2 System, in: Proceedings of the Twentieth Nobel Symposium (Ed. D. Dyrssen and D. Jagner; Almquist a n d Wiksell, Stockholm 1972), p. 147-152. [6] GAERELS, R. M., and MACKENZIE, F. T., Evolution of Sedimentary Rocks ('vV. W. Norton and Company, Inc., New York 1971). [7] GILLULY, J., WATERS, A. C., and WOODFORD, A. O., Principles of Geology (W. H. Freeman and Company, New York 1959). [8] GARRELS, R. M., and MACKENZIE, F. T., A Quantitative Model for the Sedimentary Rock Cycle, Mar. Chem. (in press). [9] SKIEROW, G., Carbon Dioxide, in: Chemical Oceanography (Ed. J. P. Riley a n d G. Skirrow, Academic Press, New York 1965). [10] RUBEY, XV. W., The Geologic History of Seawater, Bull. Geol. Soc. Am. 62, 1111-1174 (1951). [11] S*LLEN, L. G., The Physical Chemistry o/Seawater, in: Oceanography (Ed. M. Sears, American 9 Association for the Advancement of Science, Publ. 67, Washington 1961), p. 549-581. [12] SILLEN, L. O., The Ocean as a Chemical System, Science ]56, 1189-1197 (1967). [13] HOLLAND, H. D., The History of Ocean Water and its Effect on the Chemistry of the Atmosphere, Proc. Natl. Acad. Sci. 53, 1173-1183 (1965). [14] REVELLE, R., and SUESS, H. E., Carbon Dioxide Exchange between Atmosphere and Ocean and the Question of an Increase of Atmospheric CO l during Past Decades, Tellus 9, 18-27 (1957).

35/1, 1973

Carbon Dioxide System in Oceans

27

[15] ~LXN, B., On the Exchange of Carbon Dioxide between the Atmosphere and the Sea, TeiIus 72, 274-281 (1960). [16] SIEVER, R., Sedimentological Consequences of a Steady-State Ocean-A tmosphem. Sedimentology 11, 5 2 9 (1968). [17] HELGXSON, H. C., and MACKENZXE, F. T., Silicate-Seawater Equilibria in the Ocean System, Deep-Sea Res. 77, 877-892 (1970). [18] WEYL, P. K., Environmental Stability of the Earth's Surface," Chemical Considerations, Geoehim. Cosmochim. Acta 30, 663-679 (1966). [19] PYTKOWlCZ, R. M., The Chemical Stability of the Oceans, Oregon State University Tech. Rept. 214 (Corvallis, Oregon 1971). [20] MClNTYRE, C. D., and PHIMEY, H. K., Laboratory Studies of Peripkyton Production and Community Metabolism in Lotic Environments, Ecol. Monogr. 35, 237-258 (1965). [21] GARP.ELS, R. M., and MACKESZm, F. T., Sedimentary Cycling in Relation to the History of the Continents and the Oceans, in: The Nature of the Solid Earth (Ed. C. Robertson; McGraw-Hill Inc., New York 1972), p. 93-121. [22] BucIt, K., HARVEY, H. W., WAXXENBERG, H., and GRIPENBERG, S., t)ber dos KoMensaure2 system im Meerwosser, Rappt. Proc~s-Verbaux Rdunions Conseil Perm. Inter. Exploration Mer 79, 1-70 (1932). [23] CULBERSON,C., and I~TKOWlCZ, R. M., Effect of Pressure on Carbonic Acid, Boric Acid and the p H in Seawater, Lilmaol. Oceanogr. 13, 403-417 (1968). [24] KESTER, D. R., and l>x'x~rOWlCZ,R. M., Sodium, Calcium and Magnesium Sulfate Ion-Pairs in Seawater at 25~ Limnol. Oceanogr. ILl, 686-692 (1969). [25] I~TKOWXCZ, R. M., Calcium Carbonate and the i~i situ pH, Deep-Sea Res. I0, 633-638 (1963). [26] RXDFIXLD,A. C., The Exchange of Oxygen Across the Sea Surface, J. Mar. Res. 3, 347-361 (1948). [27] PY-rKowxcz, R. M., Oxygen Exchange Rates off the Oregon Coast, Deep-Sea Res. II, 381-389 (1964). [28] l~rKowlcz, R. M., DUEDALL, I. W., and CO~rNORS, D. N., Magnesium Ions: Activity in Seawater, Science 152, 640-642 (1966). [29] PX'TKOWlCZ,R. M., and KESTER, D. R., The Physical Chemistry of Seawater, in: Oceanogr. Mar. Biol. Ann. Rev. 9 (Ed. H. Barnes; George Allen and Unwin Ltd., London 1971), p. 11-60. [30] t>X'TKowlcz, R. M., Sand-Seawater Interactions in Bermuda Beaches, Geochim. Cosmochim. Acta 35, 509-515 (1970). [31] WEYL, P. K., The Solution Behavior of Carbonate Minerals in Seawater. E P R Publication 428 (Shell Development Co., Houston 1966). [32] CHAVE, K. E., and SCHMALZ,R. F., Carbonate-Seawater Interactions, Geochim. Cosmochim. Acta. 30, 1037-1048 (1966). [33] CHAVE, K. E., and SuEss, E., Suspemled Minerals in Seawater ,Trans. N. Y. Acad. Sci. Ser. (11) 29, 991-1000 (1967). [34"] REDu ~X_.C., The Biological Control of Chemical Factors in the Environment, Am. Sci. d6, 205-221 (1958). [35] HAWLEY, J., and I>XrTKOWlCZ,R. M., Solubility of Calcium Carbonate in Seawater at High Pressure and 2~ Geochim. Cosmochim. Acta 33, 1557-1561 (1969). [36] KRAUSKOPILK. B., Dissolution and Precipitation of Silica at Low Temperatures, Geochim. Cosmochim. Acta lO, 1-26 (1956). [37] BROECKER, W. S., A Kinetic Model for the Chemical Composition of Seawater, Quatern. Res. l, 188-207 (1971). [38] PYxKowIcz, R. M., and CONNORS, D. N., High Pressure Solubility of Calcium Carbonate in Seawater, Science I4xl, 840--841 (1964). [39] PYTKOWlCZ, R. M., Calcium Carbonate Saturation in the Ocean, Limnol. Oceanogr. lO, 220-225 (1965). [40] B~ERNER,R. A., Activity Coefficients of Bicarbonate, Carbonate and Calcium Ions in Seawater, Geochim. Cosmochim. Acta 29, 947-965 (1965). [41] LI, T. H., TAKAHASm, T., and BRO~SCKER,W . S., The Degree of Saturation of CaCO3 in the Oceans, J. Geophys. Res. 7d, 5507-5525 (1969). [42] BEN-YAAKOV, S., and KAPLAN, I. R., Deep-Sea in situ Calcium Carbonate Saturometry, J. Geophys. Res. 76, 722-731 (1971).

28

R. Pytkowlcz

Hydrologie

[43] CARRELS,R. M., THOMPSON, M. E., and SIEVER, R., Control of Carbonate Solubility by Carbonate Complexes, Am. J. Sci. 259, 24-45 (1961). [44] tlXVXLL•, R., and FAIRBRIDGE, R., Carbonates and Carbon Dioxide, in: Treatise on Marin~ Ecology and Paleoecology 1, (Ed. J. w . Hedgpeth, Geol. Soc. Am. Mere. 67, Washington D.C. 1957), p. 239-295. [45] CLARKX, F. W., The Data of Geochemistry, U.S. Geol. Surv. But1. 770. 770 (Washington D.C. 192r [46] MURRAY, C. M., and RXLEY, J. P., The Solubility of Gases in Distilled Water and in Seawater. I V . Carbon Dioxide, Deep-Sea Res. 18, 533-541 (1971). [47] SVERDRUP,H. U., JOHNSON,M. W., and FLXMING,R. H., The Oceans; Their Physics, Chemistry, amt General Biology (Prentice-HaU Inc., New York 1942). [48] HtlTCmSSON, G. E., The Biochemistry of the Terrestrial Atmoshere, in: The Earth as a Planet (Ed. G. P. Kuiper, University of Chicago Press 1954), p. 371--433. [49] CONWAY,E. J., Mean GeochemicalData in RelaAion to Oceanic Evolution, Proc. Royal Irish Acad. SCr. B 48, 119-159 (1942). [50] RILEY, G. A., The Carbon Metabolism and Photosynthetic Efficiency of the Earth as a Whole, Am. SCi. 32, 132-134 (1944). [51] BROECI~R, W. S., LI, Y. H., and PENG, T. H., Carbon Dioxide-,Vian's Unsee,t Artifact, in: Impingement of.Vlan on the Oceans (Ed. D. W. Hood, Wiley-Interscience 1971), p. 287-324. Address of the author: Prof. Ricaxdo M. Pytkowicz, School of Oceanography, Oregon State University, Corvallis, Oregon 97331, USA.