- Email: [email protected]
The sulphur isotope balance of the ocean: an improved model
EARTH AND PLANETARY SCIENCE LETTERS 7 (1970) 366-370. NORTH-HOLLAND PUBLISHING COME, AMSTERDAM
THE SULPHUR ISOTOPE BALANCE OF THE OCEAN: AN IMPROVED MODEL C. E. REES
Department of Chemistry, McMaster University, Hamilton, Ontario, Canada Received 10 September 1969 (Revised version received 20 December 1969) Previous explanations of the variations of the sulphur isotope composition of ocean sulphate over geological time have related them to gross changes with time of the ocean sulphate content. These explanations have disregarded the role of sulphate evaporite formation as a mechanism which (in competition with bacterial sulphate reduction) controls the net isotope fractionation in the ocean sulphate reservoir. The nature of this control is demonstrated and it is shown that in fact variations of the isotopic composition of ocean sulphate may not be unequivocally related to changes in the total sulphur content of the ocean.
1. Introduction It is the purpose of this letter to present in a preliminary form the details of an improved model for the sulphur isotope balance of the ocean. The examination of sulphur isotope ratios in marine evaporites, which were associated with ancient oceans, has revealed the general form of the time variation o f 8(ocean)* [ 1 - 7 ] . Although there is not complete agreement on the fine details of this variation most workers believe that since Cambrian times the total range of variation has been at least 20o/00, that the minimum value was + 10%o in the Permian, that a maximum value ~ +30%o was attained in the Cambrian and that from the Tertiary to the present day the value has been essentially constant at ~ +20o/00 . Estimates of mass balance in the geochemical cycle of sulphur have been made most recently by Holser and Kaplan [7]. For the present purposes it is sufficient to remark that sulphur in the oceanic sulphate reservoir comes from the re-cycling of (34S/32S) sample * 8(sample) = [ 34 32 11 X 1000%0, ( S/ S)standard standard --=troilite from Canyon Diabio meteorite.
sulphur from old evaporites and sulphide-bearing sediments and from the introduction of sulphur from volcanic and primary igneous rocks. The mechanisms by which sulphur is removed from the oceans are the formation of evaporites and the bacterial reduction of sulphate to sulphide. Imbalances between the input and output rates lead to changes in the total sulphur content of the oceans while isotopic imbalances lead to changes of 8(ocean). The dominant mechanism of sulphur isotope fractionation in nature is the reduction of sulphate to sulphide by the bacterium Desulphovibrio desulphuricans. The ratio of rates of reduction for 32S and 34S may vary widely depending on temperature, sulphate concentration, availability of metabolites, etc. [ 8 - 1 3 ] and the fractionation produced also varies between wide limits depending on whether the reduction takes place in muds in contact with ocean sulphate or in muds which are buried, where there is no mixing between the ocean reservoir and the trapped sulphates. It is proposed that one may define a fractionation factor, a, which represents the worldwide average fractionation produced by the bacteria at any given time. For model calculations one may write: 8(sulphide) = 8(ocean) - a.
THE SULPHUR ISOTOPE BALANCE OF THE OCEAN t~ is not known well and estimates range from 15 to 300/00. The isotope fractionation produced by crystallization during the formation of marine evaporites is small ( ~ 1 or 2O/o0) [3, 7] and, in view of the large uncertainties in other parameters, may be conveniently set equal to zero so that for model calculations one may write: 5(evaporite) = ~(ocean). The isotopic composition of the sulphur input to the oceans is difficult to estimate since it depends on the relative magnitudes and isotopic compositions of the evaporitic, sulphide sedimentary, igneous and volcanic contributions and so may vary with time. It is generally supposed that the variations will be small and that 6(input) may lie between 0 and +10%o [3, 7].
2. Previous models Nielsen [6] and Holser and Kaplan [7] have recently made quantitative estimates of the oceanic isotope balance and of changes with time of 8(ocean). Nielsen has postulated that the normal condition of the ocean is one where the sulphur input rate is equal to the output rate and where 8(input) is equal to 8(output). He states that in order to change ~(ocean) it is necessary to increase either the rate of bacterial sulphide formation or the input rate of sulphur to the ocean reservoir. The model of Holser and Kaplan is similar to that of Nielsen• They suppose that the deposition of ocean sulphate as evaporites may be ignored from the point of view of changes of 8(ocean) because of the small isotope fractionation involved. They consider the critical relation to be the balance between the input of light sulphur (by the long term river cycle) and the deposition of other light sulphur into new sediments (by bacterial reduction). It is argued that if the inflow a f light sulphur exceeds the outflow then ocean sulphur will become lighter (lower 8(ocean)), while if the outflow of light sulphur exceeds the inflow then ocean sulphur will become heavier (higher 8(ocean)). According to this approach changes of 8(ocean)
367
reflect changes in the total sulphate content of the ocean and require that between Cambrian and Permian times this content should have increased by nearly a factor of two and, that between Permian times and the present it should have decreased by some 30%. Regarding these variations Holser and Kaplan [7, p. 129-130] state: "The sulfur-isotope data and the geochemical calculations require large shifts in the concentration of the total sulfur in the sea. Although it is usually assumed that the composition of sea water has been substantially constant since at least the Cambrian•.. • . . such changes of sulfate concentration may have been overlooked." They go on to point out that: "The possible implications of any such changes reach far beyond the significance of the change in sulfate itself." and suggest some of these implications• They conclude the discussion of the model by stating: "Now the sulfur-isotope age curve provides the first external evidence of a variation in the nature of sea water, with which such suggestions may be tested•"
3. Improved model The objection to the above type of model is the neglect of the important process of evaporite formation. The estimates of Holser and Kaplan [7] indicate that over geological time the mass of sulphur removed from the oceans by evaporite formation has exceeded that removed by sulphide formation by more than a factor of two. While evaporite formation does not introduce appreciable isotope fractionation it nonetheless controls the net fractionation produced by the combined outflow processes• With two mechanisms competing for the removal of sulphate from sea water, one of which involves isotope fractionation (sulphide formation) and one of which does not (evaporite formation) the net fractionation produced in the sea water reservoir will depend on the relative magnitudes of these mechanisms. This may be demonstrated as follows for a system which is at the steady state:
368
C.E.REES
Let
I = 32S input rate A = 32S ocean content E = 32S evaporite formation rate S = 32S sulphide formation rate e : E/S I*, A*, E*, S* are the corresponding quantities for 34S. At the steady state, the input rate is equal to the output rate:
I=E+S I * = E * + S*.
Removal of sulphur by evaporite formation does not involve isotope fractionation: E*~=A*~. Removal of sulphur by sulphide formation introduces isotope fractionation: s * / s = (A */A) (1 - ~).
Using the above relations: I* _ E* + S*
I
E+S = (E*/E) ( e / s ) + s * / s
E/S+ 1 = (A*/A)P + ( A * / A ) ( 1 - a ) P+I = (.4*/.4) [1 So
a -g;q]-
that:
~ =
Ot 1 + p+---q-
and 6(ocean) - 6(input) = p~7_
1"
(~)
Thus, at the steady state, 5(ocean) depends on 6(input), a and P. An immediate consequence of the model is that 6(ocean) should have tended to high values in periods
when evaporite formation was of minor importance and to low values in periods of major evaporite formation. This is qualitatively the case for the Cambrian and for the Permian [14] which give the extreme 6(ocean) values mentioned earlier. It is probable that variations of the various parameters have always occurred on a short enough time scale to preclude the attainment of a true steady state. In order to determine the manner in which 6(ocean) varies with time in response to changes of input rate or other parameters it is necessary to depart from the steady state treatment and, in addition, to assume the manner in which the two output rates vary with changes of ocean sulphate content. The experiments of Harrison and Thode [10] and of Kaplan and Rittenberg [ 12] indicate that for laboratory cultures of Desulphovibrio desulphuricans the rate of sulphide production is independent of sulphate concentration for values well below the sulphate concentration of sea water. It seems reasonable to suppose that such laboratory cultures would be better supplied with nutrients than their natural counterparts so that the production of sulphides by these bacteria in nature should be rate limited by factors other than sulphate concentration. It will therefore be assumed that the sulphide production rate is independent of total ocean sulphate content but that it may have varied over geological time. Such variations would be in response to changes in parameters such as the total bacterial population, the availability of nutrients, the temperature and the number and size of suitable sedimentary sites. On the other hand it seems reasonable to suppose that the rate of evaporite formation will depend on the ocean sulphate content. Evaporite formation involves the local increase of salts' concentrations to beyond their solubilities in sea water so that increases or decreases of sulphate content should enhance or inhibit evaporite deposition. The concentration of sulphate has to be increased considerably over its average ocean value in order for precipitation to occur and this is what happens in local regions where evaporite formation takes place. An increase of the average ocean concentration should further tend to increase the concentration, and thus the precipitation rate, in such local regions. In addition such an increase of the average concentration should increase the local concentration to a level where precipitation will
THE SULPHUR ISOTOPE BALANCE OF THE OCEAN occur in other regions where previously conditions for precipitation were not quite established. It will be assumed that it is possible to assign a rate constant, KE, for evaporite formation such that E = KEA. This rate constant will depend on such parameters as temperature and the number and size of suitable evaporite formation locations and so may have varied over geological time. Using the same nomenclature as previously, the rate of change of ocean sulphate content with time is given by:
dA/dt = I - KEA - S. This may be solved to give:
A _I-SKE
[~-Ao]
e-KEt.
(2)
The corresponding equation:
A*
1"-S*
- KE
I-/'_*-S*
t~-Ao]
.
e-KEt
(2a)
may be derived in the same manner for A*. It may be seen that the model is regulatory with respect to ocean sulphate content. If the input rate is altered, A changes from A o and approaches a new steady state value, the time dependence of this approach being characterized by K E which by definition is simply E/A. The order of magnitude involved may be estimated by taking the present day ocean sulphate content (~- 1.3 X 1015 tons) and sulphur removal rate by evaporite formation ( ~ 4x 107 tons/y) which together yield a time constant of ~ 3 X 107 y. It may also be seen that an increase of I leads to an increase of A which leads to an increase of the evaporite formation rate. There is no change in the sulphide formation rate so that the effect of increasing / h a s been to increase P, and according to eq. (1), this will tend to decrease the value of ~(ocean). Eqs. (2) and (2a) may be applied for as long a time as the parameters remain constant. When a parameter changes its value, due to some change in climatic or physiographic conditions say, it is necessary to reapply the equations. If changes occur on too short a time scale for the steady state relation (1) ever to be applicable then values of 8(ocean) must of course be
369
calculated from eqs. (2) and (2a). In such cases changes of 8(ocean) will be somewhat more rapid than implied by the individual values of successive time constants since eqs. (2) and (2a) will always be applied for the initial, steep portions of their exponential time variations.
4. Summary Eqs. (1) and (2) demonstrate the main properties of the model. The steady state treatment shows that the formation of evaporites may not be neglected and that 6(ocean) is controlled by the competition between this process and the formation of sulphides. Eq. (1) makes no assumptions regarding the dependence of the output rates on the ocean sulphate content. While the practical utility of this equation is limited it does indicate the direction of changes of 6(ocean) in response to changes of input and output rates and in addition indicates the asymptotic value (which may never be reached) to which 6(ocean) will tend. When reasonable assumptions are made concerning the manner in which evaporite and sulphide formation rates depend on ocean sulphate content the time dependent eq. (2) developed above indicates that a change of input rate leads to the establishment of a new steady state where the total input rate is once more equal to the total output rate. Recognition of the importance of evaporite formation in relation to the net isotope fractionation produced in the ocean demonstrates that the assumptions of Holser and Kaplan, detailed above, may not be justified. Their contention that variations with time of 6(ocean) provide external evidence of a variation in the sulphur content of the ocean cannot be accepted without qualification. Variations of the sulphur content of the ocean, of 6(ocean) and of the rate of evaporite formation are intimately connected and any attempt to quantitatively estimate the former must take into account the latter. For example, it may be seen that increasing the sulphur content of the ocean is not the only way of decreasing 6(ocean). Eq. (1) shows that ~(ocean) may be decreased by increasing the value of P. If this is done by increasing K E and thus the rate of evaporite
370
C.E.REES
formation it may be seen from eq. (2) that the sulphur content o f the ocean will in fact decrease. Further work on the development o f quantitative calculations within the framework o f the model will be performed as part of a continuing programme of investigation in sulphur isotope chemistry. The parameter P should be susceptible to observational determination. The amount of evaporite formation in different epochs has hitherto been considered on the basis of shifts of the latitudes of evaporite formation as a function of time and of paleoclimate. Now quantitative estimates of the changes in total worldwide formation rate are required. Since the fractionation produced by bacterial sulphide formation varies widely with different conditions the estimation of 0~ as a function of time will involve the establishment of average del values of sulphides of different ages weighted by the sulphur masses involved. Such determinations will be of interest not only from the point of view o f the consideration o f the present model but also with regard to other problems in sulphur isotope geochemistry generally and to the possibility of changes with time of the composition of sea water.
Ad/fowledgements I would like to acknowledge the financial support
of the National Research Council of Canada. This work has benefited greatly from discussions with H.G.Thode and Jan Monster.
References [1] W.T.Holser, l.R.Kaplan and S.R.Silverman, Geol. Soc. Am., Spee. Papers 76 (1963) 82. [2] H.G.Thode and J.Monster, In: Khimija Zemloi Kori, vol. 2, ed. A.V.Vinogtadov (Izd. Akad. Nauk SSSR, Moscow, 1964) p. 589. [3] H.G.Thode and J.Monster, Am. Assoc. Petrol. Geologists, Mem. 4 (1965) 367. [4] F.Buschendorf, H.Nielsen, H.Puchelt and W.Ricke, Geochim. Cosmochim. Acta 27 (1963) 501. [5 ] H.Nielsen and W.Ricke, Geochim. Cosmochim. Acta 28 (1964) 577. [6] H.Nielsen, Geol. Rundschau 55 (1966) 160. [7] W.T.Holser and I.R.Kaplan, Chem. Geol. 1 (1966) 93. [8] H.G.Thode, H.Kleerekoper and D.McElcheran, Research (London) 4 (1951) 581. [9] G.E.Jones and R.L.Starkey, J. Appl. Microbiol. 5 (1957) 111. [10] A.G.Harrison and H.G.Thode, Trans. Farad. Soc. 54 (1958) 84. [ 11] N.Nakai and M.L.Jensen, Geochim. Cosmochim. Acta 28 (1964) 1893. [12] I.R.Kaplan and S.C.Rittenberg, J. Gen. Microbiol. 34 (1964) 195. [13] A.L.W.Kemp and H.G.Thode, Geochim. Cosmochim. Acta 32 (1968) 71. [14] H.Borchert and R.O.Muir, Salt Deposits (D.Van Nostrand, London, 1964).
THE SULPHUR ISOTOPE BALANCE OF THE OCEAN: AN IMPROVED MODEL C. E. REES
Department of Chemistry, McMaster University, Hamilton, Ontario, Canada Received 10 September 1969 (Revised version received 20 December 1969) Previous explanations of the variations of the sulphur isotope composition of ocean sulphate over geological time have related them to gross changes with time of the ocean sulphate content. These explanations have disregarded the role of sulphate evaporite formation as a mechanism which (in competition with bacterial sulphate reduction) controls the net isotope fractionation in the ocean sulphate reservoir. The nature of this control is demonstrated and it is shown that in fact variations of the isotopic composition of ocean sulphate may not be unequivocally related to changes in the total sulphur content of the ocean.
1. Introduction It is the purpose of this letter to present in a preliminary form the details of an improved model for the sulphur isotope balance of the ocean. The examination of sulphur isotope ratios in marine evaporites, which were associated with ancient oceans, has revealed the general form of the time variation o f 8(ocean)* [ 1 - 7 ] . Although there is not complete agreement on the fine details of this variation most workers believe that since Cambrian times the total range of variation has been at least 20o/00, that the minimum value was + 10%o in the Permian, that a maximum value ~ +30%o was attained in the Cambrian and that from the Tertiary to the present day the value has been essentially constant at ~ +20o/00 . Estimates of mass balance in the geochemical cycle of sulphur have been made most recently by Holser and Kaplan [7]. For the present purposes it is sufficient to remark that sulphur in the oceanic sulphate reservoir comes from the re-cycling of (34S/32S) sample * 8(sample) = [ 34 32 11 X 1000%0, ( S/ S)standard standard --=troilite from Canyon Diabio meteorite.
sulphur from old evaporites and sulphide-bearing sediments and from the introduction of sulphur from volcanic and primary igneous rocks. The mechanisms by which sulphur is removed from the oceans are the formation of evaporites and the bacterial reduction of sulphate to sulphide. Imbalances between the input and output rates lead to changes in the total sulphur content of the oceans while isotopic imbalances lead to changes of 8(ocean). The dominant mechanism of sulphur isotope fractionation in nature is the reduction of sulphate to sulphide by the bacterium Desulphovibrio desulphuricans. The ratio of rates of reduction for 32S and 34S may vary widely depending on temperature, sulphate concentration, availability of metabolites, etc. [ 8 - 1 3 ] and the fractionation produced also varies between wide limits depending on whether the reduction takes place in muds in contact with ocean sulphate or in muds which are buried, where there is no mixing between the ocean reservoir and the trapped sulphates. It is proposed that one may define a fractionation factor, a, which represents the worldwide average fractionation produced by the bacteria at any given time. For model calculations one may write: 8(sulphide) = 8(ocean) - a.
THE SULPHUR ISOTOPE BALANCE OF THE OCEAN t~ is not known well and estimates range from 15 to 300/00. The isotope fractionation produced by crystallization during the formation of marine evaporites is small ( ~ 1 or 2O/o0) [3, 7] and, in view of the large uncertainties in other parameters, may be conveniently set equal to zero so that for model calculations one may write: 5(evaporite) = ~(ocean). The isotopic composition of the sulphur input to the oceans is difficult to estimate since it depends on the relative magnitudes and isotopic compositions of the evaporitic, sulphide sedimentary, igneous and volcanic contributions and so may vary with time. It is generally supposed that the variations will be small and that 6(input) may lie between 0 and +10%o [3, 7].
2. Previous models Nielsen [6] and Holser and Kaplan [7] have recently made quantitative estimates of the oceanic isotope balance and of changes with time of 8(ocean). Nielsen has postulated that the normal condition of the ocean is one where the sulphur input rate is equal to the output rate and where 8(input) is equal to 8(output). He states that in order to change ~(ocean) it is necessary to increase either the rate of bacterial sulphide formation or the input rate of sulphur to the ocean reservoir. The model of Holser and Kaplan is similar to that of Nielsen• They suppose that the deposition of ocean sulphate as evaporites may be ignored from the point of view of changes of 8(ocean) because of the small isotope fractionation involved. They consider the critical relation to be the balance between the input of light sulphur (by the long term river cycle) and the deposition of other light sulphur into new sediments (by bacterial reduction). It is argued that if the inflow a f light sulphur exceeds the outflow then ocean sulphur will become lighter (lower 8(ocean)), while if the outflow of light sulphur exceeds the inflow then ocean sulphur will become heavier (higher 8(ocean)). According to this approach changes of 8(ocean)
367
reflect changes in the total sulphate content of the ocean and require that between Cambrian and Permian times this content should have increased by nearly a factor of two and, that between Permian times and the present it should have decreased by some 30%. Regarding these variations Holser and Kaplan [7, p. 129-130] state: "The sulfur-isotope data and the geochemical calculations require large shifts in the concentration of the total sulfur in the sea. Although it is usually assumed that the composition of sea water has been substantially constant since at least the Cambrian•.. • . . such changes of sulfate concentration may have been overlooked." They go on to point out that: "The possible implications of any such changes reach far beyond the significance of the change in sulfate itself." and suggest some of these implications• They conclude the discussion of the model by stating: "Now the sulfur-isotope age curve provides the first external evidence of a variation in the nature of sea water, with which such suggestions may be tested•"
3. Improved model The objection to the above type of model is the neglect of the important process of evaporite formation. The estimates of Holser and Kaplan [7] indicate that over geological time the mass of sulphur removed from the oceans by evaporite formation has exceeded that removed by sulphide formation by more than a factor of two. While evaporite formation does not introduce appreciable isotope fractionation it nonetheless controls the net fractionation produced by the combined outflow processes• With two mechanisms competing for the removal of sulphate from sea water, one of which involves isotope fractionation (sulphide formation) and one of which does not (evaporite formation) the net fractionation produced in the sea water reservoir will depend on the relative magnitudes of these mechanisms. This may be demonstrated as follows for a system which is at the steady state:
368
C.E.REES
Let
I = 32S input rate A = 32S ocean content E = 32S evaporite formation rate S = 32S sulphide formation rate e : E/S I*, A*, E*, S* are the corresponding quantities for 34S. At the steady state, the input rate is equal to the output rate:
I=E+S I * = E * + S*.
Removal of sulphur by evaporite formation does not involve isotope fractionation: E*~=A*~. Removal of sulphur by sulphide formation introduces isotope fractionation: s * / s = (A */A) (1 - ~).
Using the above relations: I* _ E* + S*
I
E+S = (E*/E) ( e / s ) + s * / s
E/S+ 1 = (A*/A)P + ( A * / A ) ( 1 - a ) P+I = (.4*/.4) [1 So
a -g;q]-
that:
~ =
Ot 1 + p+---q-
and 6(ocean) - 6(input) = p~7_
1"
(~)
Thus, at the steady state, 5(ocean) depends on 6(input), a and P. An immediate consequence of the model is that 6(ocean) should have tended to high values in periods
when evaporite formation was of minor importance and to low values in periods of major evaporite formation. This is qualitatively the case for the Cambrian and for the Permian [14] which give the extreme 6(ocean) values mentioned earlier. It is probable that variations of the various parameters have always occurred on a short enough time scale to preclude the attainment of a true steady state. In order to determine the manner in which 6(ocean) varies with time in response to changes of input rate or other parameters it is necessary to depart from the steady state treatment and, in addition, to assume the manner in which the two output rates vary with changes of ocean sulphate content. The experiments of Harrison and Thode [10] and of Kaplan and Rittenberg [ 12] indicate that for laboratory cultures of Desulphovibrio desulphuricans the rate of sulphide production is independent of sulphate concentration for values well below the sulphate concentration of sea water. It seems reasonable to suppose that such laboratory cultures would be better supplied with nutrients than their natural counterparts so that the production of sulphides by these bacteria in nature should be rate limited by factors other than sulphate concentration. It will therefore be assumed that the sulphide production rate is independent of total ocean sulphate content but that it may have varied over geological time. Such variations would be in response to changes in parameters such as the total bacterial population, the availability of nutrients, the temperature and the number and size of suitable sedimentary sites. On the other hand it seems reasonable to suppose that the rate of evaporite formation will depend on the ocean sulphate content. Evaporite formation involves the local increase of salts' concentrations to beyond their solubilities in sea water so that increases or decreases of sulphate content should enhance or inhibit evaporite deposition. The concentration of sulphate has to be increased considerably over its average ocean value in order for precipitation to occur and this is what happens in local regions where evaporite formation takes place. An increase of the average ocean concentration should further tend to increase the concentration, and thus the precipitation rate, in such local regions. In addition such an increase of the average concentration should increase the local concentration to a level where precipitation will
THE SULPHUR ISOTOPE BALANCE OF THE OCEAN occur in other regions where previously conditions for precipitation were not quite established. It will be assumed that it is possible to assign a rate constant, KE, for evaporite formation such that E = KEA. This rate constant will depend on such parameters as temperature and the number and size of suitable evaporite formation locations and so may have varied over geological time. Using the same nomenclature as previously, the rate of change of ocean sulphate content with time is given by:
dA/dt = I - KEA - S. This may be solved to give:
A _I-SKE
[~-Ao]
e-KEt.
(2)
The corresponding equation:
A*
1"-S*
- KE
I-/'_*-S*
t~-Ao]
.
e-KEt
(2a)
may be derived in the same manner for A*. It may be seen that the model is regulatory with respect to ocean sulphate content. If the input rate is altered, A changes from A o and approaches a new steady state value, the time dependence of this approach being characterized by K E which by definition is simply E/A. The order of magnitude involved may be estimated by taking the present day ocean sulphate content (~- 1.3 X 1015 tons) and sulphur removal rate by evaporite formation ( ~ 4x 107 tons/y) which together yield a time constant of ~ 3 X 107 y. It may also be seen that an increase of I leads to an increase of A which leads to an increase of the evaporite formation rate. There is no change in the sulphide formation rate so that the effect of increasing / h a s been to increase P, and according to eq. (1), this will tend to decrease the value of ~(ocean). Eqs. (2) and (2a) may be applied for as long a time as the parameters remain constant. When a parameter changes its value, due to some change in climatic or physiographic conditions say, it is necessary to reapply the equations. If changes occur on too short a time scale for the steady state relation (1) ever to be applicable then values of 8(ocean) must of course be
369
calculated from eqs. (2) and (2a). In such cases changes of 8(ocean) will be somewhat more rapid than implied by the individual values of successive time constants since eqs. (2) and (2a) will always be applied for the initial, steep portions of their exponential time variations.
4. Summary Eqs. (1) and (2) demonstrate the main properties of the model. The steady state treatment shows that the formation of evaporites may not be neglected and that 6(ocean) is controlled by the competition between this process and the formation of sulphides. Eq. (1) makes no assumptions regarding the dependence of the output rates on the ocean sulphate content. While the practical utility of this equation is limited it does indicate the direction of changes of 6(ocean) in response to changes of input and output rates and in addition indicates the asymptotic value (which may never be reached) to which 6(ocean) will tend. When reasonable assumptions are made concerning the manner in which evaporite and sulphide formation rates depend on ocean sulphate content the time dependent eq. (2) developed above indicates that a change of input rate leads to the establishment of a new steady state where the total input rate is once more equal to the total output rate. Recognition of the importance of evaporite formation in relation to the net isotope fractionation produced in the ocean demonstrates that the assumptions of Holser and Kaplan, detailed above, may not be justified. Their contention that variations with time of 6(ocean) provide external evidence of a variation in the sulphur content of the ocean cannot be accepted without qualification. Variations of the sulphur content of the ocean, of 6(ocean) and of the rate of evaporite formation are intimately connected and any attempt to quantitatively estimate the former must take into account the latter. For example, it may be seen that increasing the sulphur content of the ocean is not the only way of decreasing 6(ocean). Eq. (1) shows that ~(ocean) may be decreased by increasing the value of P. If this is done by increasing K E and thus the rate of evaporite
370
C.E.REES
formation it may be seen from eq. (2) that the sulphur content o f the ocean will in fact decrease. Further work on the development o f quantitative calculations within the framework o f the model will be performed as part of a continuing programme of investigation in sulphur isotope chemistry. The parameter P should be susceptible to observational determination. The amount of evaporite formation in different epochs has hitherto been considered on the basis of shifts of the latitudes of evaporite formation as a function of time and of paleoclimate. Now quantitative estimates of the changes in total worldwide formation rate are required. Since the fractionation produced by bacterial sulphide formation varies widely with different conditions the estimation of 0~ as a function of time will involve the establishment of average del values of sulphides of different ages weighted by the sulphur masses involved. Such determinations will be of interest not only from the point of view o f the consideration o f the present model but also with regard to other problems in sulphur isotope geochemistry generally and to the possibility of changes with time of the composition of sea water.
Ad/fowledgements I would like to acknowledge the financial support
of the National Research Council of Canada. This work has benefited greatly from discussions with H.G.Thode and Jan Monster.
References [1] W.T.Holser, l.R.Kaplan and S.R.Silverman, Geol. Soc. Am., Spee. Papers 76 (1963) 82. [2] H.G.Thode and J.Monster, In: Khimija Zemloi Kori, vol. 2, ed. A.V.Vinogtadov (Izd. Akad. Nauk SSSR, Moscow, 1964) p. 589. [3] H.G.Thode and J.Monster, Am. Assoc. Petrol. Geologists, Mem. 4 (1965) 367. [4] F.Buschendorf, H.Nielsen, H.Puchelt and W.Ricke, Geochim. Cosmochim. Acta 27 (1963) 501. [5 ] H.Nielsen and W.Ricke, Geochim. Cosmochim. Acta 28 (1964) 577. [6] H.Nielsen, Geol. Rundschau 55 (1966) 160. [7] W.T.Holser and I.R.Kaplan, Chem. Geol. 1 (1966) 93. [8] H.G.Thode, H.Kleerekoper and D.McElcheran, Research (London) 4 (1951) 581. [9] G.E.Jones and R.L.Starkey, J. Appl. Microbiol. 5 (1957) 111. [10] A.G.Harrison and H.G.Thode, Trans. Farad. Soc. 54 (1958) 84. [ 11] N.Nakai and M.L.Jensen, Geochim. Cosmochim. Acta 28 (1964) 1893. [12] I.R.Kaplan and S.C.Rittenberg, J. Gen. Microbiol. 34 (1964) 195. [13] A.L.W.Kemp and H.G.Thode, Geochim. Cosmochim. Acta 32 (1968) 71. [14] H.Borchert and R.O.Muir, Salt Deposits (D.Van Nostrand, London, 1964).