The global sedimentary redox cycle

The global sedimentary redox cycle

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The global sedimentary redox cycle
Kump, Lee R.
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Tampa, Florida
University of South Florida
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xv, 245 leaves. : ill. ; 29 cm


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Biogeochemical cycles ( lcsh )
Diagenesis ( lcsh )
Dissertations, Academic -- Marine Science -- Doctoral -- USF ( FTS )


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Thesis (Ph. D.)--University of South Florida, 1986. Bibliography: leaves 214-228.

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University of South Florida
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University of South Florida
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020679808 ( ALEPH )
15740855 ( OCLC )
F51-00168 ( USFLDC DOI )
f51.168 ( USFLDC Handle )

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THE GLOBAL SEDIMENTARY REDOX CYCLE by Lee R. Kump A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Marine Scien c e in the University of South Florida August, 1986 Major Professor: Robert M. Garrels, Ph.D.


Graduate Council University of South Florida Tampa, Florida CERTIFICATE OF APPROVAL Ph.D. Dissertation This is to certify that the Ph.D. Dissertation of Lee R. Kump with a major in Marine Science has been approved by the Examining Committee on June 6 1986 as satisfactory for the dissertation requirement for the Ph.D. degree. Examining Committee: Major Professor: Robert M Garrels, Ph.D. Member: Albert C. Hine, Ph.D. Member: (16\ Dennis Kir'wan, Ph. D Member: J. Ph. D


ACKNOWLEDGEMENTS The journey to this point in my began long ago. I of owe it all to my who of my question "how come?". My high school science Dave Astin of Minneapolis, c. then of the of Chicago and now at SUNY Stony and Eugene A. Shinn of the United States Geological at Island, Miami all played in my development. I would like to my to the of my committee, R. H. A. C. Hine, A. D. and J. J. Walsh guidance the last five and of this My accomplished the impossible he had the patience and ability to me a who had no idea of what he was talking about to one who could at least his suggestions and ideas into code, the model, and the I join a long list of scientists who owe much of and success in science to the tutelage of M. Finally I would like to single out my wife Michelle as the most in my life. She not only my late nights and weekends at the lab but in the as well. and accumulating knowledge in the geosciences allowed me to use as a sounding technician, and ii


More importantly, her emotional support and enthusiasm for my w ork made the process of acquiring my degree an enjoyable experience. Financial support over the last five years has come from a number of sources, including the National Association of Geology Teachers, the U.S. Geological Survey, the Department of Marine Science at the University of South Florida, the Poynter Fund, grant EAR 8306390 from the National Science Foundation and a subcontract from NASA to Northwestern University. iii


TABLE OF CONTENTS LIST OF TABLES vi LIST OF FIGURES vii ABSTRACT xiii INTRODUCTION CHAPTER 1. THE CARBON AND SULFUR CYCLES AND ATMOSPHERIC OXYGEN 13 The Isolated Carbon-Oxygen Cycle 13 The Isolated Sulfur Cycle 22 The Coupled Carbon-Sulfur-Oxygen System 30 Preliminary Model Results for the Last 100 my 46 Summary 54 CHAPTER 2. THE MODIFIED BLAG MODEL AND ITS APPLICATION TO THE MIOCENE PHOSPHOGENIC EPISODES 57 Tectonics Climate, and the Global Geochemica l Cycle 63 The Present-Day System 66 General Kinetic Equations and the Operation of the Model 77 Results and Discussion 81 Tentative Interpretations of the Miocene World 120 Summary 132 CHAPTER 3 THE GLOBAL IRON CYCLE 137 Sedimentary Iron Reservoirs 139 Weathering Rates 144 Iron in Modern Sediments and Early Diagenesis 152 Deep Burial, Metamorphism, and Iron Reduction 160 The Global Iron Cycle 172 T e mporal Trends in the Ferrous/Ferric Ratio of Sedimentary Rocks 176 Summary 186 CHAPTER 4. FURTHER EXTENSIONS AND IMPROVEMENTS OF THE MODEL 187 The Incorporation of the Iron Cycle 187 The Sediment Cycle and Carbon Isotopes 199 SUMMARY WITH EXTENSIONS 208 Summary of Chapter 1 208 Summary of Chapter 2 209 Summary of Chapter 3 210 Summary of Chapter 4 211 Future Considerations 212 iv




LIST OF TABLES Table 1. Functional Relations among Fluxes and Reservoirs of the Carbon-Oxygen System 19 Table 2. Functional Relations among Fluxes and Reservoirs of the Sulfur-Oxygen System 29 Table 3. Model Calculations of Calcium Carbonate Saturation 74 Table 4. General Kinetic Equations 78 Table 5. Modern Iron Reservoir Sizes 140 Table 6. Sedimentary Iron Distribution 142 Table 7 Iron Weathering Fluxes 146 Table 8. Iron Oxidation During Weathering 147 Table 9. Iron-Kerogen Reactions 173 Table 10. Carbon Isotopic Value of the Carbonate Weathering Flux Through Time Base d on the Sediment Cycling Model 207 vi


LIST OF FIGURES Figure 1. Isotopic records of marine sulfate and inorganic carbon. 4 Figure 2. 20 m.y. average values of (1a) and o13C (1b) for the last 700 m .y. 7 Figure 3 Prediction of of the ocean from the o13C curve 1 0 Figure 4 A representation of the average Phanerozoic configuration of the simplified carbon cycle. 15 Figure 5. The response of o13C of the ocean to an instantaneous increase in the burial rate of organic carbon 24 Figure 6. A representation of the average Phanerozoic configuration of the simplified sulfur cycle. 26 Figure 7. A representation of the average Phanerozoic configuration of the coupled carbon and sulfur cycles. 32 Figure 8. The isotopic response of the coupled carbon-sulfur system to a sudden increase in organic carbon burial. 35 Figure 9. The response of the oxidation-weathering rates of the reduced sedimentary reservoirs to the perturbation from steady state. Figure 10. The responses of the sedimentary gypsum and organic carbon reservoirs to the sudden increase in organic carbon burial imposed on the coupled carbon-sulfur system Figure 11. (A.) The response of the atmospheric reservoir size vii 37 40


of 02 to the instantaneous increase of the CH20 burial rate and increase or decrease of the FeS2 burial rate; (B.) The predicted time course of the slope between o13C and of the ocean following a sudden increase in organic carbon burial. 42 Figure 12. The isotopic records of oceanic and o13C for the last 100 m.y., from Lindh (1983) and Shackleton (1985), respectively. 48 Figure 13. calculated values of the burial rate of organic carbon (F45) and and the atmospheric 02 level for the last 100 m.y. Figure 14. The calculated relationship between the rates of organic carbon and pyrite sulfur (F31) burial 50 for the last 100 m.y. 53 Figure 15. The isotopic and geologic records of change in the global geochemical cycle during the Cenozoic. 59 Figure 16. Box model of the present-day, global, long-term geochemical cycle, adapted from Lasaga et al., 1985. 68 Figure 17. The model sensitivity of the pyrite reservoir size to the variation in mean o13C of the carbonate reservoir and to the form of the gypsum burial rate equation Figure 18. The model sensitivity of the gypsum reservoir size to the variation in mean o13C of the carbonate reservoir and to the form of the gypsum burial rate equation. Figure 19. The model sensitivity of the oceanic sulfate viii 84 86


reservoir size to the variation in mean 613C of the carbonate reservoir and to the form of the gypsum burial rate equation. Figure 20. The model sensitivity of the oceanic calcium reservoir size to the variation in mean 613C of the carbonate reservoir and to the form of the gypsum burial rate equation. Figure 21. The model sensitivity of the organic carbon reservoir size to the variation in mean 613C of the carbonate reservoir and to the form of the gypsum burial 88 90 rate equation. 93 Figure 22. The model sensitivity of the burial rate of CH20 to the variation in mean 613C of the carbonate reservoir and to the form of the gypsum burial rate equation. 95 Figure 23. The model sensitivity of the burial rate of pyrite S to the variation in mean 613C of the carbonate reservoir and to the form of the gypsum burial rate equation. Figure 24. The model sensitivity of the oceanic Mg reservoir size to the variation in mean 613C of the carbonate reservoir and to the form of the gypsum burial 97 rate equation. 101 Figure 25. The model sensitivity of the atmospheric 02 reservoir size to the variation in mean 61 3C of the carbonate reservoir and to the form of the gypsum burial rate equation Figure 26. The model sensitivity of the calcite and dolomite ix 103


reservoir sizes to the variation in mean o13C of the carbonate reservoir and to the form of the gypsum burial rate equation. Figure 27. The model sensitivity of the burial rate of calcite to the variation in mean o13C of the carbonate reservoir and to the form of the gypsum burial rate equation. Figure 28. The model sensitivity of the oceanic bicarbonate reservoir to the variation in mean o13C of the carbonate reservoir and to the form of the gypsum burial rate equation. Figure 29. The model sensitivity of the atmospheric C02 reservoir size to the variation in mean o13C of the carbonate reservoir and to the form of the gypsum burial rate equation. Figure 30. Model sensitivity of atmospheric 02 to 10% variation in the weathering rate constants, land are a and spreading rate correction factors and to 106 108 110 112 5% variation in E c and in E s 115 Figure 31. Demonstrated relationship between o13C and the ratio of the volumes of terrigenous and marine sediment deposited in a given period. Figure 32. Model run with Kominz (1984) spreading rate curve showing the calculated burial rate of organic c. Figure 33. Model run with Kominz (1984) spreading rate curve showing the calculated burial rate of pyrite S. Figure 34. Model run with Kominz (1984) spreading rate curve X 119 122 124


showing the calculated level of atmospheric 02 Figure 35. Model run with Kominz (1984) spreading rate curve showing the calculated level of atmospheric C02 Figure 36. Model run with Kominz (1984) spreading rate curve showing the calculated weathering rate of of the MgSi03 reservoir. Figure 37. Model run with Kominz (1984) spreading rate curve showing the calculated oceanic pH. Figure 38 A,B. Modern soil profiles of Fe11!Fe111 ; A. o n shalederived till and B. a laterite on dolerite. Figure 38 C,D. Paleosol profiles of Fe11/Fe111; C late Paleozoic paleosol on granodiorite and D. 127 129 131 134 149 Mid-Proterozoic paleosol on meta-arkose. 151 Figure 39. Global distribution of chlorite and Fe11/Fe111 in modern, oceanic surface sediments. 154 Figure 40. Relationship between Fe11/Fe111 and weight percent organic C in modern, oceanic surface sediments. 159 Figure 41. Relationship between weight percent K20 and Fe11!Fe111 for a variety of mixed-layer clays. 164 Figure 42. Relationship between weight percent K20 and Fe11!Fe111 in the Precambrian lutites. Figure 43. Data from various boreholes on A) Fe11!Fe111 and B) the geothermal gradient. Figure 44. Relationship between Fe11/Fe111 and temperature at depth in the crust. Figure 45. Schematic of the global Fe redox cycle sho wing the relationships between weathering and oxidation, xi 166 169 171


burial and reduction. 175 Figure 46. Temporal trends in Fe111Feiii through geologic time. 178 Figure 47. Calculated Phanerozoic trends in Fe11/Feiii using two methods, one based on the surviving sedimentary mass and its relative abundances of platform and geosynclinal sediments and the other based on a modified constant ocean-atmosphere model with two transfer reaction stoichiometries. Figure 48. Results of modified SLAG model run with the Fe-silicate cycle showing the calculated weathering and burial/reduction rates of the ferrous-silicate reservoir. Figure 49. Results of modified SLAG model run with the Fe-silicate cycle showing the calculated burial rate of organic C compared to the results of the similar run of Chapter 2 without the Fe cycle. Figure 50. Results of modified SLAG model run with the Fe-silicate cycle showing the calculated atmospheric 02 mass compared to the results of the similar run of Chapter 2 without the Fe cycle. Figure 51. Results of modified SLAG model run with the Fe-silicate cycle showing the ratio of the burial rates of reduced and oxidized iron. Figure 52. The observed and calculated age distribution of the global Phanerozoic sedimentary mass. xii 184 194 196 198 201 205


TiiE GLOBAL SEDIMENTARY REDOX CYCLE by LeeR. Kump An Abstract Of a dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Marine Science in the University of South Florida August, 1986 Major Professor: Robert M. Garrels, Ph.D. xiii


A model of the global redox cycles of carbon, sulfur, and iron is used to assess the impact of these cycles on atmospheric 02 Flux relations are developed which allow a rapid response of the rate of oxygen consumption to an increase in 02 production. Perturbation of the burial rate of organic C (CH20) leads to the rapid attainment of a new, steady, 02 level; however, transfer of material among the sedimentary reservoirs continues for millions of years. The oceanic isotopic response of carbon is rapid; that o f sulfur sluggish. This fact accounts for much of the character of the observed relationship between o34S and o13C through the Phanerozoic The C and S redox subunits are app ended to a comprehensive geochemical cycling model. The model sensitivity is tested; 02 is most sensitive to the isotopic parameters which determine the values of the burial fluxes of pyrite and CH20. Model results highlight the Miocene as an unusual time ; low oceanic pH and the accumulation of salinity prior to and high burial rates of CH20 during t he Miocene may have had a role in the phosphogenic and evaporitic episodes of this time The global cycle of iron begins as iron is oxidized during weathering and deposited in the ocean as ferric iron. Little iron is reduced during early diagenesis. With increased burial temperatures the ferric iron in clays is reduced by CH20. The amount of Fe reduced depends on the burial temperature achieved. The observed increase through time in the oxidation state of iron in sedimentary rocks is interpreted as a predominantly secondary feature r eflecting increased xiv


metamorphism of older rocks. The modeled iron fluxes have a significant effect on 02 The inadequacies of the present model are most acute for the calculations based on the isotopic composition of the sedimentary reservoirs. An alternative is presented that models the decreased probability of erosion of a sedimentary unit after it has been tectonically folded. The results are promising; the mean weathering flux cS 13C changes slowly through time and can thus be approximated reasonably well. Abstract approved: Major Professor: Robert M. Garrels, Ph.D. Professor, Department of Marine Science June 6, 1986 XV


INTRODUCTION This dissertation describes the development of a box model of the global sedimentary redox cycle. Like earlier versions, this model is dependent on a variety of constraints including the stable isotope records of carbon and sulfur, the principles of closed-system cycling and a steady-state configuration, and several assumptions concerning rate laws of weathering and deposition. It goes a step further by including the atmosphere as a distinct 02 reservoir subject to change based on the imbalance of fluxes to and from it, and by considering the redox cy cle of non-pyritic iron. Thus, a new set of unknowns is created and a number of additional constraints must be stipulated. These will be developed in the course of the discussion. These additions to the model are made so that the nature of the coupling between the C, S and Fe sub cycles that comprise the global sedimentary redox system may be investigated and possible excursions in atmospheric 02 assessed. Earlier quantitative attempts to describe the Phanerozoic exogenic redox cycle were guided by the recognition that, because long term oxygen and C02 demands by the operation of the sedimentary cycle are so large compared to the atmospheric reservoir of these compounds, it should be possible to describe the sedimentary cycle in terms of constant atmospheric composition. Garrels and Perry ( 1974) compo sed a global redox reaction whereby any net oxygen demand by the operation of the carbon cycle was balanced


2 by an equivalent net 0 2 supply by the operation of the sulfur cycle. The coupling was direct so the response of one subcycle to the other was instantaneous. The reduction of oxidized C to CH2 0 (a generic formula for organic carbon) was considered to be accompanied by the oxidation of pyrite S to sulfate in gypsum, according to the reaction: 4 FeS2 + 8 CaC03 + 7 MgC03 + 7 Si02 H20 (1) Note that this reaction is written without the production or consumption of gases. It provides a way by which large-scale transfer between reservoirs can occur while maintaining an atmosphere tolerable to complex life. Perhaps the best evidence that large transfers among sedimentary reservoirs have occurred through geologic time is provided by the isotopic records of oceanic sulfur and carbon preserved in evaporites and carbonates, respectively (Figure 1 ) Isotope ratio differences between the oxidized and reduced reservoirs of C and S exist because of the selective utilizati on and removal of the light isotopes 12C and 32S during CH2 0 and FeS2 production and burial. During the Paleozoic the ocean became progressively enriched in 1 3C and depleted in 3 4 S through the preferential removal of oceanic C to the CH20 rather than to the CaC03 reservoir (increasing the reservoirs' isotopic difference), and through the delivery of oceanic S to the CaS04 rather than to t he FeS2 reservoir (decreasing the isotopic difference between the two sulfur reservoirs) The imbalance of burial fluxes caused the global transfer reaction (eq 1) to proceed from left to right. After the Paleozoic the trends reversed. The ocean became depleted in 13C and enriched in 34S as the transfer reaction (eq. 1) proceeded from right to left. Figure 2


Figure 1. Isotopic records of marine sulfate and inorganic carbon. A. The sulfur isotopic record of marine evaporites in /00 relative to the Canyon Diablo Troilite standard. B. The carbon isotopic record of marine carbonate in /00 relative to the Peedee Belemnite standard. Both curves taken from the compiled data of Holser (1984) who gives further references.


4 0 I a b T 100 .... .... _, as 200 w 300 (!) <( 400 ,, ;---_-_, ( 500 -----s 600 +10 20 3Q-2 -o+ 2 4 b34s sulfate, b 13c carbonate, %oCDT %o PDB


5 plots 20 m.y. averages of the o13C curve against that of the curve. There is a general inverse relationship between the two variables as pointed out by others (Veizer Holser, and Wilgus, 1980; Lindh, 1983; Holland, 1984), yet in detail a cyclical pattern with clockwise and counterclockwise excursions between them emerges Holland ( 1973) used the sulfur isotope age curve of Holser and Kaplan ( 1966) and a series of mass balance and flux relations to calculate the net 02 flux resulting from the operation of the sulfur cycle. An analogous set of calculations for the carbon cycle was not possible because of the incomplete o 1 3C record available at that time; without the 02 fluxes from the carbon cycle, Holland was unable to assess the nature of Phanerozoic variations in atmospheric oxygen levels. An attempt to assess oxygen fluxes by Schidlowski, Junge, and Pie trek ( 1977) assumed a constant 0 2 flux from the carbon cycle and ascribed imbalances derived from the sulfur cycle to oxidation-reduction relations of iron and changes in atmospheric 02 Later calculations by Schidlowski and Junge ( 1981 ) with the revised o 1 3C curve of Veizer, Holser, and Wilgus (1980), approximately balanced the 02 fluxes between the C and S cycles and relegated the iron cycle to lesser importance A more detailed, constant ocean-atmosphere, carbon-sulfur-oxygen model was developed by Garrels and Lerman (1981), modified by Berner and Raiswell (1983), and recalculated by Garrels and Lennan ( 1984). Garrels and Lerman used the transfer stoichiometry of Garrels and Perry (1974) to couple the sulfur cycle with the carbon cycle. With first-order weathering-rate laws and the constraints of total mass and isotope conservation, they produced a computer model that could estimate the


Figure 2. 20 m.y. average values of o3"S (1A) and o13C (1B) for the last 700 m.y. (values for 600 to 700 m.y. are approximations from data in Lindh, 1983)


3 I 0 2 20 m y AVERAGES 1 0 -20m. y 2 20-40m.y . 33 640-660m.y. 34 660-680m. y I 7,{? a Q 4() 1 0 -1 10 20 b34s%o 21 --..:)


8 sizes of, and fluxes to and the and oxidized of and time. The Garrels and Lerman models also permitted calculation of oceanic cS 3 "S values from the cS 1 3C When these values a typical model run plotted against each other (Figure 3) the resulting graph bears strong resemblance to the observed relations of cS 13C and cS 3 "S shown in Figure 2. Thus, deviations about a ..... !--- .' .. --. .. line" do not to non-compensatory variations in the carbon and cycles. Instead, the constant between rapid carbon isotope to environmental changes and the slow sulfur isotope changes buffered by the large oceanic sulfate reservoir. Despite the success of constant ocean-atmosphere models in predicting the abundance of pyrite, carbon, and gypsum in the and in one isotopic the they do notqictate that the ocean and have remained constant through geologic time. Recent modeling has this issue by what the major of and oceanic composition and how the feedback mechanisms operate to keep the compositions within limits. Based on "the of of the various conditions, plus what (they) as deductions, plus a few guesses," Lerman, and Ma.ckenzie (1976) determined a of functional between fluxes and of the C-S-0 system that used to model the effects of of a steady-state system on atmospheric 02 and C02 These included:


Figure 3. Prediction of o 3 .. S of the ocean from the o 1 3C curve (Figure 1 B) and the Garrels and Lerman ( 1984) constant atmospheric 02 model. Note similarity to Figure 2.


0 0 C') .... .0 +4 I .... +3-11'1" II +2 +1 0 -1 10 15 NUMBERS C ORRESPOND TO POINTS ON F IGURE 1 C ............. AND ARE THE AGE IN 106 YRS +20 \. 20 b34s %o 0


1) first-order oxidation rates of the reduced reservoirs with respect to their sizes; 2) an inverse relationship between 02 levels and the fraction of the total photosynthetic organic carbon that sur-vives the trip to the seafloor and to final burial in the sediments; 3) a dependence of pyrite production on both the organic carbon sedimentation flux and the size of the oceanic sulfate reservoir; 4) maintenance of saturation of the ocean with respect to CaC03 11 These relations created a negative feedback system in which perturbations from a steady-state condition, e.g. increased erosion rates or doubled photosynthetic rates were rapidly compensated for and a new steady state achieved within a few million years. Using the same modeling strategy, Garrels and Berner ( 1983) and Berner, Lasaga and Garrels (1983) constructed a computer model of the global carbonate -silicate geochemical cycle (henceforth SLAG). The processes they considered included the weathering of carbonates and alkaline earth silicates o n land, the deposition of caC03 in the sea, the removal of Mg as seawater cycles through oceanic hydrothermal centers, and the production of alkaline earth silicates during subduction and metamorphism. Using a detailed set of flux relations corrected for spreading rate, global temperature, and land area available for weathering, they were able to show the effects of these processes on atmospheric C02 levels as well as on the Ca, Mg, and HC03 concentrations in the ocean


12 Their model was later extended to include the processes important to the redox cycle of the Earth (Lasaga, Berner, and Garrels, 1985). The effect of including the S and organic C cycles on C02 levels was significant; however, their treatment of 02 as a "passive" reservoir, i.e., without influence on pyrite or CH20 weathering rates, led to unreasonable calculated 02 levels for the geologic past. The modeling described in this work was motivated by the continued need for a quantitative model of the global redox system that could calculate atmospheric 02 levels and be compatible with the kinetic approach of the BLAG model. The first chapter details the steps taken to develop such a model of the global carbon and sulfur cycles. This chapter is a modified version of Kump and Garrels (1985, 1986). In the second chapter the model is incorporated into BLAG and the combined system is applied to the study of the unique conditions that led to the Miocene phosphogenic episodes. The third chapter describes the global iron cycle a part of the overall redox cycle that is poorly understood yet intensively studied. The fourth chapter considers the incorporation of the iron cycle in the modified BLAG model of Chapter 2 and provides an improved assessment of the temporal c hanges in the mean isotopic composition of the carbonate reservoir. The final chapter provides an overview of the global cycle and makes suggest i ons for improvements of the model.


13 CHAPTER 1. THE CARBON AND SULFUR CYCLES AND ATMOSPHERIC OXYGEN The model developed in this chapter is an extension of that presented by Garrels and Lerman (1984); specifically, the instantaneous 02 flux-balance coupling between the C and S cycles is removed and the 02 level is regulated by its interaction with these cycles. The uninterrupted existence of complex life for the last half billion years or more requires model flux relations which provide a fast response of the C and S cycles to changes in atmospheric 02 This response is tested by the application of an arbitrary perturbation an increase in the rate of organic C burial first to the isolated C cycle, to test the response time of the ocean o13C, and then to the coupled C-S system, to investigate the efficacy of the indirect coupling approach. Finally, the model is applied to the isotope records of C and S for the last 100 m.y. and a preliminary Cenozoic 02 cu r ve is produced. The Isolated Carbon-Oxygen Cycle Steady State Figure 4 is the average configuration of the Phanerozoic carbon cycle synthesized from many sources. It represents an admixture of estimates of modern reservoir sizes and fluxes, with calculated values designed to balance the system and create a "steady state" under which there is no net transfer of materials (including isotopes) from one


Figure 4. A representation of the average Phanerozoic configuration of the simplified carbon cycle. Note units for reservoir sizes and fluxes.




16 sedimentary reservoir to another. The sizes of the reservoirs are given in units of 1018 moles, and are reasonably representative o f those that have been used by modelers in the past. The transfers between reservoirs are in units of 1018 moles per m y., and are subscripted to indicate the source and terminus for each flux. The assumption that the modern condition approximates the Phanerozoic average is bolstered by the fact that the present values of ocean o 13C and o 3 .. S are approximately the Phanerozoic mean values; pre-Devonian values lie to one side of the mean, post-Devonian values on the other. Because it is known that these curves reflect the configuration of the C-S system, it is reasonable to assume that the late Proterozoic, Devonian and Holocene represent times when the system was close to its average configuration. The Carbon Cycle The equal fluxes of 02 and CH20 (organic matter) from the combined ocean-atmosphere inorganic carbon reservoir are the net resu l t s of photosynthesis on land or in the sea expressed as: C02 + H20 CH20 + 02 ( 2 ) The net CH20 buried is expressed as that preserved per unit time in sediments, until uplift and re-erosion, and is the 3.5 x 1 018 moles per m.y. of organic carbon burial described by the flux F .. 5 The organic matter produced by photosynthesis averages about 25 I 0 0 lighter than the o13C of HC03 in the sea (Deines, 1980). The addition of 02 to the atmosphere via CH20 burial (F ,.7 ) is compensated by the oxidation of organic carbon during weathering and metamorphism ( F75). This oxidation yields C02 that returns to the ocean-atmosphere, F 5 .. and replenishes


17 the C02 used during net photosynthesis. The weathering of limestone is usually written: 2+ CaC03 + C02 + H20 Ca + 2 HC03 (3) The stream flux of bicarbonate to the sea is half from CaC03 and half from atmospheric C02 The latter makes no net contribution to the combined ocean-atmosphere C reservoir and is not included in the carbonate weathering flux The metamorphism of CaC03 is not explicitly considered here, but is essentially included in F 6.,. The addition of ea2+ and HC03 to the sea increases their oceanic concentration and CaC03 is precipitated to maintain ocean saturation Limestones are deposited with virtually the same o13C as that of the ocean. In developing relationships between reservoir sizes and their fluxes the principle of the conservation of elements ( and their isotopes) and the approximation of constant oceanic inorganic C content are applied. The former can be expressed as: + M5 + M6 = constant (4) where Mi represents the mass in moles of C of the i th reservoir, with i=4 ,5, and 6 corresponding to the oceanic inorganic C and sedimentary CH20 and CaC03 reservoirs, respectively, and (5) where oi represents the o13C of the ith reservoir. The approximate constancy of the ocean inorganic C reservoir, is assumed because of the small size of the reservoir and the fact that it could quickly be exhausted by a slight excess of C deposition over input by weathering. The actual mechanism that regulates in nature is the maintenance of oceanic CaC03 saturation (see discussion in Chapter 2),


18 here emulated by constraining to be constant with time In Chapter 2 this constraint will be removed. Flux Relations (Table 1) For the purposes of this chapter it is assumed that changes in the depositional rete of organic carbon (CH20) drive the carbon cycle and indirectly drive the sulfur cycle; the perturbation from the steady-state configuration is an instantaneous increase in the depositional rate of CH20 from its steady-state value of 3.5 x 1018 to 4 5 x 1018 moles per m.y. (relation 1, Table 1) Relation 2 is the primary extension of this model from earlier, constant 02 models. It states that the weathering rate of CH20 an oxidation reaction, is proportional to both the amount of material available (M5 ) and the amount of 02 in the atmosphere (M7). At the present atmospheric oxygen level, virtually all of the reduced sedimentary organic carbon and pyrite sulfur exposed to the atmosphere is oxidized during weathering, and there is little detrital sulfide or fossil organic carbon in sediments. At lower oxygen levels it is conceivable that this conversion would be less than complete (Holland, 1978). At higher oxygen levels several processes may act to increase oxygen consumption: 1) the penetration of 02 into soils may be greater because of increased diffusional rates (Howeler and Bouldin, 1971) or to increased pumping of oxygen into soils by plant respiration (Raskin and Kende, 1985); 2) the oxic / anoxic front in groundwaters may deepen as 02 levels increase;


Table 1 Functional Relations a.rrong Fluxes and Reservoirs of the Carbon-Oxygen Sys tem (Refer to Figure 4) 18 6 1. F45 = F47 = moles/10 yr 2. F 5 4 = F75 = k54M5M7 k54 = (106 yro18moles)-1 -3 6 -'-1 3. F64 = k64M6 k64 = 2 .69x10 (10 yr) F46 = F54 + F64 -F45 5. d(M4o4)/dt-= o5F54 + o6F64-

20 3) higher 02 levels may lead to increased soil C02 pressures by the increased activity of aerobic bacteria; the enhanced attack of carbonic acid on rocks would increase weathering rates, thus, exposing fresh, reduced rocks to oxidation. This relationship between 02 and oxidation rates provides for a much faster response of the weathering of CH20 to an increase in burial rate (and 02 production) than would otherwise be achieved if the weathering rate were only responding to the slow growth of M5 In a sense the carbon fluxes respond on a time scale commensurate with the residence time of 02 in the atmosphere, rather than to that of the much larger sedimentary reservoirs (Lasaga, 1980). Another way in which the C cycle may be coupled to atmospheric 02 is through an inverse relationship between atmospheric (and thus, perhaps deep-ocean) 02 levels and CH20 burial rates, F .,5 (Holland 1978). To develop a flux relation for F.,5 however, will require that the global nutrient cycles be incorporated into the model, a task saved for future consideration. Relation 3 expresses a simple first-order relationship between limestone weathering and its reservoir size. In the "BLAG" model (Berner, Lasaga, and Garrels, 1983; Lasaga, Berner, and Garrels, 1985), that considers all the major controls of C02 magmatism, metamorphism and volcanism -C02 i s calculated explicitly and its effect on CaC03 weathering is linked through the greenhouse effect on temperature Relation 4 simply reflects the conservation of mass and constant ocean C concentration constraints. Fluxes into the ocean are balanced by fluxes out. Relation 5 expresses the response of the ocean isotopic composition


21 to the flux of isotopes into and out of the ocean. For our model = 0, so relation 5 can be written: + (6) but: (7) so: + + (8) where c is the isotopic fractionation factor for organic carbon production (=25/00). The time rate of change of is thus a function of the C fluxes to and from the ocean and the difference between their isotopic values and Relations 6 and 7 state at length that the rate of change in size of the sedimentary reservoirs is the difference between the fluxes in and out. Relations 8 and 9 are similar to relation 5 and indicate that the mean isotopic value of the sedimentary reservoirs responds to the fluxes in and out of the reservoir and to their isotopic compositions There is no distinction made between old and new material; the reservoir is homogenized instantaneously. This is a controversial relation, but it seems to describe the crude first-order system Many of the inconsistencies of current modeling may be ameliorated by a more realistic approach to the relation between the time of deposition of sed iments and the time a t which they are exposed to erosion (see Chapter 4). Finally, relation 10 shows that there is a net gain in 02 when the burial rate of CH20 exceeds its oxidation rate and a net loss when the converse occurs Relation of 613C to Fluxes


22 These relations can be incorporated into a computer model, and the response to an increase in can be generated, given the steady-state values as initial conditions. Doing so, and incrementing by 105 years, the response shown in Figure 5 was produced, as was instantaneously increased from 3.5 x 1018 to 4.5 x 1018 moles per m.y., and then held constant. A new constant value for the ocean o 1 3C is achieved in a million years; most of the isotope change is complete within 0.5 m.y. With slightly different initial conditions and a doubling of F 5 Holland (1978) calculated the response time to be 105 years. At this stage of the model analysis, the response of the carbon isotopic composition of the ocean to a change in the fluxes of carbon to and from the ocean is considered to be instantaneous and the term is thus zero. Later, this term is reinstated and the isotope curves are used to drive the model. In nature, changes in the burial rate of organic carbon are continuous and undoubtedly less abrupt. o 1 3C keeps pace with these changes; thus it is a good indicator of trends in the burial rate of organic carbon. The rest of the system takes longer to respond (see Figures 8 through 11) and probably never has sufficient time to adjust to a new, total-system steady state. The Isolated Sulfur Cycle Figure 6 depicts the steady-state configuration of the exogenic sulfur system. Sulfide sulfur, found mainly as pyrite in shales, is oxidized to sulfate (F 71) by atmospheric and dissolved oxygen, and is carried by the streams (where it is joined by the sulfate from gypsum


Figure 5. The response of o13C of the ocean to an instantaneous increase in the burial rate of organic carbon from 3.5 x 1018 to 4.5 x 1018 moles per million years, calculated over 100,000 yr intervals.


(00 I a) Je:1 1 ap c 0 CD .,..... .-4 +> 0 _o L :J N +) "' .-4 L L OJ > Q_Ln QJ 0 mU8 c .,..... (f) OJ E .,..... 2 4


Figure 6. A representation of the average Phanerozoic configuration of the simplified sulfur cycle. Same units as Figure 4.



27 dissolution, F23) to the ocean (Fl 3). The return of the gypsum sulfate is the result of evaporation of seawater in basins peripheral to the oceans which (F 3 2 ) The return of sulfur to the sulfide reservoir requires the bacterially-mediated reduction of sulfate by organic matter (Berner, 1962, 1984; F31) according to the schematic reaction: 2-2 Fe20a + 8 + 15 CH2 0 + C02 4 FeS2 + 16 HC03 + 7 H 2 0 (9) Because 32S is preferentially used during this process, pyrite sulfur is about 35 I 0 0 lighter than the o HS of the ocean from which it formed (s=35/00, the value used by Garrels and Lerman, 1984). The oxygen produced during pyrite production is a result of photosynthesis (eq. 2); CH2 0 is produced, and then deposited in anoxic sediments where bacteria oxidize it to HC03 by reducing por-e-water sulfate. Because 0 2 is not used to oxidize the or-ganic matter-, it remains in the atmosphere as free o xygen. The oxidized inorganic carbon produced during sulfate reduction balances that which was consumed during photosynthesis (in the current model no distinction is made between the various forms of oxidized carbon in the combined ocean -atmosphere reservoir). The reaction that represents the net effect of sulfate reduction and pyrite production for time scales greater than a few years is thus: 2 Fe2 0 3 + 8 + 16 C02 + 8 H 2 0 4 FeS2 + 16 HCOa + 15 0 2 (10) The numerical model of the sulfur cycle operates under a set of constraints identical to that o f the carbon cycle. Total mass is conserved: ( 11 ) where M represents the mass in moles of S of the i th reservoir, with 1 i =1,2, and 3 corresponding to the sedimentary FeS2 and oceanic


28 reservoirs, respectively. Total isotopic composition is also conserved, such that: M1o1 + M2o2 + M3o 3 =constant (12) where oi represents the of the ith reservoir. A rather unattractive constraint, constant ocean sulfate reservoir size (dM3/dt = 0), is also imposed despite the near certainty that M3 has varied considerably over geologic time. Lasaga, Berner, and Garrels (1985) tested this constraint versus an alternative, treating M3 as a known function of time, and found little sensi ti vi ty of the pyrite burial flux to M3 This constraint could be removed if the information provided by the S isotope record were incorporated into the model and the depositional rate of gypsum was treated as a known function of time based on the known abundance of preserved evaporites of various ages as advocated by Holser, Maynard, and Cruikshank (1984) ; this alternative will be evaluated in Chapter 2 Flux Relations (Table 2) The relation of F 3 1 the pyrite depositional flux, to F 5 the organic carbon depositional flux, is one of the most difficult aspects of the modeling (Berner, 1982, 1984). Raiswell and Berner (1985) have demonstrated that in euxinic environments the pyrite percentage of the total sediment is relatively high but is essentially independent of the organic carbon percentage. In normal marine sediments (defined by Berner and Raiswell (1983) as those deposited from oxic waters) pyrite percentage is proportional to organic carbon percentage in a mole ratio of about 0.13. In sediment deposited from fresh waters the pyrite percentage is very low and, as in euxinic environments, is nearly


29 Table 2. Functional Relations a.rrong Fluxes and Reservoir's of the Sulfur"-Oxygen System (Refer" to Figur"e 6) F32 = F13 + F23 F31 (106yr"018moles) 1 ( 1 06yr') -1 d(o 3 MJ)Idt = F13o 1 + F23o 2 -F31 ( o 3 -Es) F32o 3 ctM1 /ctt z F31 -F13 ctM2 /ctt = F32-F23 wher'e Es = 35 00 ct(o1 M1 )/dt = Co3-Es)F31 o 1 F13 ct(o2M2 )/ctt = o 3 F32 o 2 F23 ctM7 /ctt z 15/8(F31-F13) = (F37-F71)


30 independent of organic carbon content. The response of pyrite burial rates to the model perturbation (an increase in F .. s ) could, thus, range from a large decrease to a large increase in the flux; both possibilities are tested. The values of F31 chosen are about double and half the steady-state value, i.e. 1.0 x 1018 and 0.25 x 1018 moles per m.y. (Table 2, relation 1). The relations between fluxes and reservoirs of the isolated S cycle are analogous to those of the C cycle. The pyrite (FeS2 ) reservoir weathers in proportion to its size and to that of the 02 reservoir (relation 2). The gypsum (CaSO .. ) reservoir weathers only in proportion to its size (relation 3). The other relations of Table 2 are directly analogous to those of Table 1. In relation 10, the 15/8 factor arises from the stoichiometry of the sulfate-reduction reaction shown above. The Coupled Carbon Sulfur -Oxygen System When the isolated sulfur cycle is attached t o the carbon cycle the resulting coupled system (Figure 7) is sufficient to explain major changes in the C and S isotopic values of seawater and in the level of oxygen in the atmosphere If oxygen is to remain relatively constant, any net increase (or decrease) in demand on 02 by the operation of the ca rbon cycle must be nearly balanced by a net decrease (or increase) in demand on 02 by the operation of the sulfur cycle. The response of one c y cle to the other must be fairly rapid, or 02 levels will either rise or fall to unacceptable levels. The functional relations of the coupled system are simply the sum of Tables 1 and 2 The coupling occurs through the shared influence of the C and S cycles on the 02 reservoir and through the imposed relation


Figure 7. A representation of the average Phanerozoic configuration of the coupled carbon and sulfur cycles. Same units as before.


Ytru RESERVOIR 10 18 MPLES FLUXES 10 18 MOLES/10 6 YR BER OXIDATION PYRITE 180 s F 31 0 21 Fes2 b34s=-15%o BURIAL CD F 13 0.53H 2S04 0 13Fe 2 o3 WEATHERING GYPSUM 2+ 2-F23 1 0 Ca so4 200 s b34s=+20%. F32 1 0 CaS04 BURIAL ---ATMOSPHERIC 02 38 (j) (\1 ('I 0 0 10 .... NET () ...... PHOTOSYNTHESIS .... (f) u. OCEAN (+ATMOSPHERIC C02) 40 so 24 3.31NORG. C 14 ca2 + b13c=+t.3.._ 0 f75 3 5 02 OXIDATION f45 3 5 CH20 BURIAL F54 3 5 C02 2+ 2-F64 10.5 Ca ,C03 F46 10 5 Caco3 BURIAL ORGANIC C 1aoo b13c=-23.7 3900 Caco3 w 1\)


33 between F31 and Coupled-System Response to the Perturbation The same perturbation from steady state as before applied to the isolated C cycle was applied to the coupled C-S-0 system. F 5 was arbitrarily increased and then held at 4.5 x 1018 moles per m.y. (from the steady-state value of 3.5 x 1018 moles per m. y.), and the model response was calculated over 1 m.y. increments. The results revealed that the approach to a new steady state occurs on three different time scales: a one-million-year response time derived from the turnover time of oceanic C, a 30-40 m.y. response time resulting from the atmospheric 0 2 response, and a hundreds of millions of years response time from the slow turnover of the sedimentary reservoirs. The effect of the perturbation on ocean isotopic values is shown in Figure 8. o 1 3 C responds "instantaneously", peaking at the value attained in Figure 5 for the isolated response of the ocean to increased F 5 Over the next 30 m.y. c 13C drops as F 5 (Figure 9a) increases rapidly towards a balance with in reponse to the rapid attainment of a new steady-state 0 2 level (Figure 11 a). The drop in o 1 3 C is more pronounced for the increased F31 case because of the larger increase in 0 2 due to the combined effects of increased CH2 0 and FeS2 burial rates. The oceanic sulfur isotope ratio does not respond quickly because of the buffering effect of the large reservoir mass of oceanic For the case where F31 is increased, increases as 32S is preferentially removed to the FeS2 reservoir. The opposite trend is produced when F31 is decreased from the steady-state value. Ocean isotopic steady state is nearly achieved for both elements within the response time of


Figure 8 The isotopic response of the coupled carbon -sulfur system to a sudden increase in organic c arbon burial (and increase or decrease in pyrite production, F31) A. The response of the oceanic carbon isotopic ratio. B. The response of the oceanic sulfur isotopic ratio.


35 0 0 0 c 0 0 CD +) 0 ...0 L cc --:) 0 o.w """ ; ; (0 ; ; 0...(0 Q) 0 a 0 u .....-4 "'-..../ c r-4 CJ) QJ a 0 E C\1 C\1 +) < CD 00 a 00 (T) -JEt Tap SvE 1ap C00 I o)


Figure 9. The response of the oxidation-weathering rates of the reduced sedimentary reservoirs to the perturbation from steady state. A. The weathering rate of organic carbon, B. The weathering rate of pyrite sulfur, F13


0 0 -> -0 CD 0 (() 0 0 N 0 lf') . (T") < m vS .:J E t .:J (..JA eOI/ScTOUJ et01) 0 c 0 g .-4 -+-) 0 ..0 L J 0-+-) (() L L QJ > 0....(0 QJ 0 0 u: c .-4 (f) QJ o E N .-4 37


38 atmospheric 02 Although F s .. changes little after about 30 m.y., its value is not that of F .. s ( 4. 5 x 1018 rroles per m. y.), and the CH20 reservoir continues to grow (for de creased F 3 1 ) or diminish (for increased F 3 1 ) through the rest of the run (Figure 10a). The change in 02 indicated by the growth or diminution of the CH20 reservoir is effectively counterbalanced after 30 m.y. by an opposite change in 02 production resulting from the diminution (with decreased F 31) or growth (with increased F31) of the FeS2 reservoir (and thus, conserving total sulfur, the complementary growth or diminution of the easo .. reservoir, Figure 1 Ob) F 5.. and F 1 3 then slowly approach F .. 5 and F 3 1 over hundreds of millions of years by the gradual transfer of C from the CH20 to the CaC03 reservoir and of S from the caso .. to the FeS2 reservoir (under the condition of increased F3 1 ; the reverse transfer occurs for the case of decrease d F 31). !my net release of 02 by the C cycle is completely co mpensated for by the net c onsumption of 02 by the S cycle, and vice versa. This slow process under constant 02 levels i s in essence the constant atmosphere condition of earlier models (Garrels and Lerman 1981, 1984; Berner and Raiswell, 1983). The Correlation Between o13C and o34S The general negative correlation between the o13C of marine carbonates and the o 3 4S of marine evaporites through time has been recognized as an indication of the net transfer of oxygen between the carbon and sulfur cycles (see Introduction and Figure 2) Variation about a linear correlation has often been partially attributed to a poor isotope record; thus, it has been assumed that all points ideally could


Figure 10. The responses of the sedimentary gypsum and organic carbon reservoirs to the sudden increase in organic carbon burial imposed on the coupled carbon-sulfur system.


1350 u I u c 0 r"\ ffi1300 (/) L ru 0 r-4 0 1275 E 0 m 250 ...... 0 I .......... (f) .........., E :J (/) Q_ A m 175 0 A. 8. 20 20 time 40 F3t F3a l 60 80 40 60 80 s1nce perturbation Cl06 yr) 100 100 J::" 0


Figure 11A. The response of the atmospheric reservoir size of 02 to the instantaneous increase of the CH20 burial rate and increase or decrease of the FeS2 burial rate. B. The predicted time course of the slope between o13C and of the ocean following a sudden increase in organic carbon burial.


42 0 0 0 I 0 -c t0 r-i ..w 0 _o L :J 0 r o.,w """ iii co co L L I.&. QJ > t--Q_(O QJ 0 0 0 u t--"It '-/ "It c r-i t--(/) QJ 0 < --> 0 E (\J t--N iii iii r-i u.. u.. ..w t-I I 1-d, < CD 00 U10 U1 0 0 U1 (l) I (SoTOUJ et01) 0 20 sow-:+o 0 JEt-JEt


43 fall on a straight line (Veizer, Holser, and Wilgus, 1980; Lindh, 1983; Holland, 1984) Using the functional relationships of the. model presented here we can calculate the values of c13C and representing different steady states (Lerman, pers. comm. 1985). The slope of ( 15) Here the subscript ss denotes the steady-state values, indicates the difference in reservoir sizes between the old and new steady states, the 15/8 term derives from the stoichiometry of the transfer reaction, the E terms are the fractionation factors for carbon and sulfur, and ST and CT are the total amounts of sulfur and carbon in the system. If no 02 is produced or consumed, the steady-state slope is: dc13C = -0.11 (16) ss ss Figure 11b plots the time course of the slope between c13C and and their initial values following the perturbation in The instantaneous response of c 13C is evident in the early positive and negative peaks in the slope but is quickly damped out as o13C and approach their new steady-state values. Within 30 m.y. these values are closely approached, and the slope assumes the value predicted by the above equation (with a slight correction for the production of 02 ) The difference in response times between C and S may explain the near vertical excursions in Figure 2. During these periods fluctuations in may have been so rapid that the S system had insufficient time to respond. The counterclockwise paths of the plots in Figures 2 and 3 also can be the result of the differences in oceanic isotopic response between C and S. c13C responds quickly to flux c hanges; an increase in the burial


44 rate of organic carbon, for example, would cause an initial t vector on the isotope plot. As the sulfur cycle responds to balance the 02 fluxes it drives its isotopic value in the opposite direction, in this example in the direction. With a decrease in CH 20 burial, the vectors are o13C followed by The result is a counterclockwise path. Clockwise rotation, as observed in Figure 2 for the late Proterozoic to early Paleozoic (from an incomplete, mostly inferred isotopic record, however), requires either that the response time of o 3 was shorter than that of o13C (from either a small oceanic reservoir or extremely large S fluxes) or that the C and S cycles were not operating to buffer, but rather to rapidly change, atmospheric 02 The lack of unusual evaporitic sequences from this time period argues that perhaps the second explanation is more likely. The crude negative correlation between the observed values of o 1 3C and o in sedimentary carbonates and sulfates is apparently produced b y the relatively rapid adjustment of the ocean s isotopic composition to environmental changes Deviations about a singl e correlation line exist because of the following: 1) the possibility of changes in ST, CT, Ec' andEs; 2) the production and consumption of 02; 3) fast, non steady-state e nvironmental changes reflected in 4) the difference in response times of o13C and Feedbacks in the Coupled System The feedbacks that drive the system towards a new steady state after the applied perturbation are inherent in the response of the c ycles of


45 carbon and sulfur to a change in 0 2 level. For the carbon cycle, an increase in CH20 burial leads to initial growth of both the 0 2 and CH2 0 reservoirs. Quickly at first, in response to the increasing 0 2 level, and then gradually, owing to the slow growth of the CH20 and/or 02 reservoirs, the weathering rate of CH2 0 increases, putting a drag on the rise of the atmospheric 0 2 level and leading eventually to a balance with the burial flux of CH20. The response of the carbonate reservoir mirrors that of the CH2 0 reservoir because of the conservation of total carbon. For the sulfur cycle the feedback is somewhat different. For the model run in which F 3 1 is decreased and F .. 5 increased, the weathering rate of FeS2 does not decrease immediately to approach steady state; instead it increases in response to rising 0 2 levels. This produces a significant drag on the 0 2 reservoir so that within 30 m.y. the 0 2 fluxes are virtually balanced. The new steady-state 0 2 level is lower than that which would be pro duced by the response of the isolated C cyle to an increase in F .. s (i.e. a nearly-proportional i ncrease in 0 2 to =49 x 1 0 1 8 moles) The large imbalance in fluxes to and from the FeS2 reservoir leads to a decrease in reservoir size, and once constant 0 2 levels are achieved, the weathering rate of FeS2 begins to diminish. Slowly, then, flux balance is approached in the S cycle, while material continues to be transferred between the oxidized and reduced reservoirs. With an increase in the rate of pyrite burial accompanying the perturbation of the carbon cycle, the sulfur cycle responds similarly to the carbon cycle. F13 rises rapidly at first, and then slowly approaches F 3 1 as the C-S-0 system approaches steady state. The new, steady-state 0 2 level is higher than in the case of decreased F31' and


46 higher than that calculated for the response of the isolated c cycle to the perturbation. In other words, for an inverse relationship between F 31 and F .. s, an increase in 0 2 production by the carbon cycle is countered by the sulfur cycle, whereas for a direct relationship betwee n the fluxes, an increase in 0 2 production by the carbon cycle is augmented by the sulfur cycle. Preliminary Model Results For The Last 100 m.y. In the application of the coupled C-S-0 model to the real world, two options have to be considered: 1) use of o13C and o 3 .. S records to run the model, Which allows the relationship between the CH2 0 burial rate, F .. 5 and the pyrite production rate, F31, to be calculated, or, 2) use of the o13C record plus an assumed relationship between F .. s and F31 to predict the sulfur isotope record. Figure 12 shows versions of the observed isotope values of C in marine carbonates (Shackleton, 1985) and S in marine evaporites (Lindh 1983) that are used here to produce the results presented in Figure 13, according to the first option above. The burial fluxes of pyrite sulfur and organic carbon are now expressed as: F .. s (do .. ldtM .. F5 .. (os-o .. ) -F6 .. (o6-o .. ))/c F31 (do 3/dtM3-Fl3(ol-<53) F23(<5z-<53))/s ( 17) ( 18) where the derivatives with respect to time of 013C and <53 .. 8 are derived from Figure 12, and the numbers refer to the reservoir designations in Figure 7 The other relations of Tables 1 and 2 still apply. Figure 13 depicts the model results for atmospheric Oz levels and


Figure 12. The isotopic records of oceanic and o13C for the last 100 m.y., from Li ndh (1983) and Shackleton (1985) respectively, used in the model to generate Figure 13.


48 ,...... L 0 0 >-. (() 0 ,.--. '-./ 0 0 (() (()w C) < 0 0 CD CD


Figure 1 3 Calculated values of the burial rate of organic carbon and the atmospheric 02 level for the last 100 m .y. (labelled K+G), based on the isotopic records of C and S from Figure 12. The model results of Shacklet o n (1985) are shown f o r comparison (labelled S).


50 /"'""\ L 0 0 >.... lJ + (() 0 ,...-1 \,./ 0 0 (() (Ow lJ < 0 0 (I) (I) (88TOLU st01) (....JA g01/S8TOW et01) 20 sv .::1


51 the CH20 burial flux (F .. s) for the last 100 m.y. Shackleton's (1985) results are plotted for comparison. Both models predict slowly increasing F .. s for much of the Tertiary, a peak in the middle Miocene, and a trend towards lower fluxes for the post-Miocene. The divergence in the two predictions of 02 levels is due to the absence of the S cycle in Shackleton's model. The increase in o34S from 100 to 10 m.y. demands an excess of pyrite production over weathering for this period. This 02 production is by no means trivial, and must be considered. Because the model is run backwards in time, and is pinned on modern conditions, the 02 production during that 90 m.y. period requires a much lower 02 level at 70 m.y. than that predicted by Shackleton. Organic carbon Pyrite Sulfur Burial Relations Figure 14 demonstrates the calculated relationship between F45 and F 3 1 Notice that they are somewhat positively correlated for low F 31 and F4 5 uncorrelated at high F45, and inversely correlated at high F31 One can account for this pattern by considering the depositional locus theory of Berner and Raiswell ( 1983 ) This theo ry proposed that the locus of CH20 bur ial has shifted through Phanerozoi c time, from normal marine environments, where the rate of CH20 deposition is approximately seven and one half times the rate of pyriteS deposition (moles C/S=7.5; Berner, 1982), to euxinic or to non-marine environments, where C / S is considerably lower (Leventhal, 1983; Raiswell and Berner, 1985) or higher, respectively. Their model of the carbon-sulfur system necessitates, as do all constant 02 models, an inverse relationship between F45 and F31 under all depositional regimes. Here the constant-02 constraint has been removed, and the results now suggest


Figure 14. The calculated relationship between the rates of organic carbon (F45) and pyrite sulfur (F31 ) burial for the last 100 m.y., based on the isotopic records of C and S from Figure 12 and the rrodel presented in this paper. The points were plotted for each 1 m.y. increment.


53 /""\ 5.0 L I I A co 0 .. _... )( )0( )( n 4. 0 i;1 en 01 ,....... f x I 0 )()( )( E )( )( xx m 3. 0 ._ x)( _. 0 .,. _... )( '-/ lll I 2. 0 I I lL 0. 0 o. 5 1.0 F31 <1018 moles/106 yr)


54 that the relationship between these fluxes also depends on the dominant depositional environment Under normal marine conditions, increases in CH20 burial are accompanied by increases in FeS2 production, and vice-versa, as observed in modern sediments and as discussed above. Under nonmarine conditions, CH20 burial proceeds without significant pyrite production (see e.g. Berner and Raiswell, 1983) so that changes in the former are not reflected by the latter. Under euxinic conditions, increases in FeS2 production are not accompanied by increases in CH20 burial, and CH20 burial rates may be low. Thus we suggest a positive relationship between and F31 applies for normal marine conditions, and a negative or non-correlation applies to other times Furthermore when the average, global, CH20 depositional environment is either non-marine or euxinic, the C and S cycles may be more or less compensatory, and 02 fluctuations may only be moderate. Under normal marine conditions, however the C and S cycles store or release oxygen in concord, and 0 2 fluctuations may be significant. The inverse relationship predicted by the constant 02 models may be representative of only a segment of Phanerozoic time; at other times, large variations in atmospheric 02 may have occurred although these may have been constrained by feedbacks not in the present model (e. g Watson et al., 1978). These conclusions are the result of current modeling, and give some targets for future research. Summary A box model of the global sedimentary redox cycle has been constructed that permits calculation of the response of atmospheric 02


55 to changes in the rates of deposition and weathering of reduced c and S, given the isotopic records of C and S and a reasonable set of constraints. Forerrost arocmg these constraints is the imposed proportional relationship arrong the weathering fluxes of the reduced reservoirs and their masses and the mass of 02 in the atmosphere 02 is thus an active reservoir that provides a coupling between the carbon and sulfur cycles. Perturbing the steady-state C-S system by instantaneously increasing the burial rate of CH20 yielded the following insights into the operation of the global cycle: 1) o13C of the ocean responds within 1 m y then readjusts as the sulfur cycle and which must turn over a much larger oceanic reservoir, responds sluggishly. Rapid fluctuations in the C cycle may go unrecorded in the isotopic record of the S cycle. 2) Atmospheric 02 responds fairly quickly to the perturbation through the action of the coupled cycles of C and S, and attains a new, higher, steady, value while the transfer of material between the reduced and oxidized sedimentary reservoirs continues, very slowly approaching a new, total system steady-state. In nature, this final condition is probably never realized. A preliminary attempt to apply the model to the real world was found to be reasonably consistent with the modeling results of Shackleton (1985), that showed a drop in 02 levels through the Neogene. The calculated burial rates of CH20 and FeS2 for this period are positively correlated when the rates are low, in agreement with observations of


56 modern sedimentary systems, and are uncorrelated or inversely related at higher values. This suggests two things: 1) The global ratio of pyrite production to organic C burial is dependent on environment of deposition. In normal marine settings the relationship is positive, and 02 changes can be significant, while in non-marine or in euxinic environments it is either negative or uncorrelated, with less net effect on atmospheric 02 2) Oxygen levels have undoubtedly varied considerably during the Phanerozoic.


CHAPTER 2 THE MODIFIED BLAG MODEL AND ITS APPLICATION TO THE MIOCENE PHOSPHOGENIC EPISODES 57 This chapter is primarily devoted to the expansion of the global redox rrodel developed in Chapter 1 into a rrore comprehensive, global geochemical rrodel akin to the BLAG model (Berner et al., 1983). In doing so it is interesting to consider an application of the model to a particular cycling problem namely the conditions which led to the unique occurrences of phosphorite, evaporite and organic carbon during the Miocene. Several isotopic and geologic records of the Cenozoic highlight the Miocene as a time of minima or maxima, of turnarounds and excursions in values. A representative case is the isotopic record of marine sulfate, preserved in evaporites (Figure 15A; Lindh, 1983) Throughout the Paleogene and early Neogene, (the standardized ratio of in the ocean) increased, rising from an early value,of 17 /00 in the Paleocene to a peak val ue of 22 /00 in the Miocene. The value then fell to the present oceanic value of 20 00 This pattern may be related to the dearth of Tertiary and abunda n ce of Miocene evaporites (Helser 1984) According to Ronov (1982) the Miocene evaporite mass exceeds that of the entire Paleogene The i mplications for global ocean chemistry will be discussed below Another significant Miocene maximum was achieved in the isotopic record of marine inorganic carbon ( o 1 3C) preserved in CaCO 3 deposits


Figure 15. The isotopic and geologic records of change in the global geochemical cycle during the Cenozoic A. The isotopic ratio of to 32S in marine evaporites, expressed as parts per thousand relative to the Canyon Diablo Troilite (CDT) standard (Lindh 1 983). B. The isotopic ratio of 13C to 12C in marine carbonates, expressed as parts per thousand relative to the Peedee Belemnite (PDB) standard (S, Shackleton 1985; L, Lindh 1983). C. The isotopic ratio of 180 to 160 in marine carbonates expressed as parts per thousand relative to PDB (P, planktonic, B, benthic foraminifera; Shack leton and Kennett 1975; graph taken from Vincent and Berger, 1985) D. The global, mean, ocea n floor spreading rate in cm/yr (Kominz, 1984) E Eustatic sea-level in m relative to today (Vail and Hardenbol, 1979) F. The isotopic ratio of radiogenic 8 7Sr to stable 8 6Sr in marine carbonate rocks (Palmer and Elderfield, 1985)


" Q: >., 0 .... v l1J t!) < deal ss (0 / 00 COT) 20 25 epraading rote

60 (Figure 158). Lindh's (1983) 613C curve displays a less impressive peak in the Miocene than does that of Shackleton ( 1985), whose data show a peak that is the culmination of a slow increase in 613C throughout the Tertiary. Both curves drop sharply from the Miocene to the Recent. Figure 15C records the oxygen isotopic composition of marine planktonic and benthic foraminifera ( cf. Shackleton and Kennett, 1975; Berger et al., 1981; Vincent and Berger, 1985). The Miocene displays a re-initiation in the Cenozoic trend towards increasing o 180 which was abandoned during the Oligocene. The global rate of sea-floor spreading as a function of time has been calculated based on the age distribution of the seafloor and an analysis of the paleo-poles of plate rotations (cf. Southam and Hay, 1977; Pitman, 1978; Kominz, 1984). The global mean spreading rate curve of Kominz (1984; Figure 150) shows a large drop during the early Eocene, fluctuating rates during the Miocene, and a gradual rise to the present value from the late Miocene minimum. Vail and Hardenbol (1979) have produced a detailed Tertiary eustatic sea-level curve based largely on the stratigraphic interpretation of seismic data. As shown in Figure 15E, the Paleogene was a period of high global sea level that oscillated about a slowly decreasing mean of around 150-200 m above the present level. The most dramatic Cenozoic sea-level event occurred in the late Oligocene when sea level fell more than 200 m in a few million years or less. Sea level then rose to a small early Miocene maximum, fell slightly, then rose steadily to a major middle Miocene maximum of about 120 m above present at a time when there was extensive deposition of phosphorites in Florida and North Carolina (Riggs, 1984). The late Miocene was a time of continual fall


61 in sea level. A sharp spike in the sea-level curve appears in the early Pliocene which coincides with another phosphorite event (Riggs, 1984); the dramatic Pleistocene swings in sea level are not shown in this plot. Finally, Figure 15F (Palmer and Elderfield, 1985) shows the stable isotopic ratio of radiogenic 87Sr to 86Sr in carbonate rocks, a measure of the relative importance of continental weathering rates over inputs from marine hydrothermal activity. During the Paleogene, this ratio slowly increased; after and perhaps as a result of the tremendous sea-level fall of the late Oligocene it began to increase rapidly, assuming a new, larger, steady value in the late Miocene. In the post-Miocene Cenozoic, 87Sr/86Sr began to increase again. Today's ratio is the highest achieved during the entire Cenozoic. In sunnnary, the middle Miocene was a time in which peaks were observed in o31+S, o 13C, 87Sr/86Sr, eustatic sea level and mean, global sea-floor spreading rate and in which a trend t owards increasing o 180 was initiated. Although it is tempting to relate these c urves intuitively to changes in global geochemical cycling, productivity and climate, the intricate interdependence of the various processes involved necessitates the use of quantitative models to unravel the responses of the global system to the changes indicated by the curves. A computer model that includes the major influences on the global carbonate -silicate geochemical cycle was developed by Garrels and Berner (1983) and Berner et al. (1983). This model (SLAG) predicted atmospheric C02 levels based on calculations of the relative rates of produ ction of C02 during magmatism, metamorphi sm, and caC03 precipitation, and consumption during rock weathering.


62 Lasaga et al. (1985) refined the BLAG model by inserting the global, geochemical, redox cycles of sulfur and organic carbon, based on the work of Garrels and Lerman (1981,1984). In the model of Lasaga et al. (1985 ) additional C02 fluxes arose due to the consumption of C02 during net photosynthesis and its production during the oxidation of fossil organic carbon. Their version of the carbon-sulfur subsystem did not allow the rapid response of the weathering of reduced sedimentary components (FeS2 -pyrite, and CH2 0 -fossil organic carbon) to changes in atmospheric 0 2 ; thus, unreasonable 0 2 levels were calculated. In Chapter 1 (and in Kump and Garrels, 1986) this problem was addressed by assuming that the weathering rates of FeS2 and CH2 0 are proportional to the amount of 0 2 in the atmosphere. The simple model of the C-S subsystem in Chapter 1 does not consider the effects of C02 or land area on weathering rates, but rather is based entirely on the isotopic records of C and S and the principle of conservation of mass. In this chapter, the BLAG model is modified in several ways, as will be discussed below. First, a slightly altered, present-day configuration of the global carbonate -silicate -organic carbon -sulfur geochemical system is constructed. Then, the relationship between 0 2 and weathering rate developed in Chapter is incorporated into the model. Next, the simplifications of the isotope balance equations in Lasaga et al. (1985) are removed; all fluxes and their isotopic compositions are now included. Oceanic sulfate mass is allowed to vary based on an imposed gypsum depositional rate function inferred from the abundance of preserved evaporites. For the latter runs, a new flux relationship is developed for the depositional rate of calcite that strictly maintains oceanic saturation with respect to CaC03


63 To simplify the analysis of the effect of these modifications on the model results, the linearly decreasing spreading-rate function has been applied to all model sensitivity runs (see B LAG; Parsons 1982), whereby spreading rate decreases linearly from a value 20% larger than today's at 100 mybp to the present val ue The model is first ru n over the last 100 my for three different initial carbonate-reservoir carbon isotope values and for two versions of the gypsum depositional rate function, in order to assess the sensitivity of the model results to these factors. For these runs the original calcite depositional rate function was used The sensitivity of the calculation of atmospheric 02 to the assumed rate constants and fractionation factors is then tested by varying these parameters by +/10 % and 5 %, respectively. A discussion of organic carbon burial follows that considers the effect of changes in the burial rates of terrestrial and marine organic carbo n on the global depositional rate of CH20 and on o 13C of the ocean Finally, the implications for interpretations of the Neogene world are addressed and are facilitated by one final model run in whic h the spreading rate curve of Kominz (1984) is used. Tectonics, Climate and The Global Geochemical Cycle Climate And Weathering The BLAG geochemical model and the extension presented here do not utilize all of the historic records presented in Figure 15. In particular, variations in global mean t e mperatures and continental weathering rates, reflected in the isotopic records of oxygen and strontium, respectively (e .g. Veizer, 1983), are not part of the model.


64 Thus these records can be used as independent checks of the rrodel results if the reasons for their secular trends are well understood The response of 61e0 to global temperature changes arises from the temperature dependence of the isotopic fractionation of oxygen (Urey, 1947) Other factors influence the sedimentary carbonate o 1e0 including changes in oceanic o 1 eo due to continental ice buildup or melting (cf. Emiliani, 1 955; Shackleton and Opdyke, 1973), biological "vi tal" effects on the fractionation factor (Urey et al., 1951), and isotopic exchange during carbonate diagenesis (see summary in Bathurst, 1975). If these factors are isolated from consideration, it is possible to assi gn temperatures corresponding to the o 1 eo values of Figure 15F, with rrore negative values (to the right) indicating warmer global temperatures. Higher temperatures are assumed to lead to increases in weathering rates as a result of the stimulation of microbial activity in soils; aerobic bacteria oxidize soil organic carbon to C02 'Whic h is then consumed during rock weathering. In the BLAG model the global mean temperature is calculated from the mass of atmospheric C02 via a "greenhouse" equation. The obvious alternative would be to use o1e0; with the current model however 61e0 merely serves as a test of the predicted tempe rature. The relationship between continental weathering rate and 87Srf86Sr is complicated by variations in isotopic exchange during the circulation of seawater through seafloor hydrothermal systems, in the source of Sr during weathering, and in the diagenetic release of Sr from marine sediments The global average river water 87Sr/86Sr is =0.711 (Wadleigh et al. 1985) while the hydrothermal Sr flux has a ratio of =0. 704


65 (Elderfield and Greaves, 1981). In general, then, high seawater values of 87Sr/86Sr have been taken to indicate high continental weathering rates relative to the rate of hydrothermal isotopic exchange at mid-ocean ridges (of. Peterman et al., 1970; Brass, 1976; Burke et al., 1982; Veizer, 1983; Palmer and Elderfield, 1985). The Global Feedback System An intricate web of feedbacks exists between atmospheric and oceanic composition, continental weathering, marine sedimentary deposition, subduction and hydrothermal activity. For example, Garrels and Berner (1983) and Berner et al. (1983) have concluded that the primary control of atmospheric C02 is tectonics. Production of C02 occurs during the subduction and decarbonation of carbonate sediments during metamorphism; C02 is consumed during continental weathering. The level of C02 in the atmosphere regulates temperature in a non-linear fashion, according to the "greenhouse" principle. Temperature in turn affects weathering rates; thus an increase in C02 leads to a global warming and increased consumption of C02 during weathering. However, if increases in C02 are largely due to increases in the rates of subduction and decarbonation, and if in turn, these are a function of oceanic sp reading rates, the net effect of increased weathering rates due to high C02 and thus high temperature may be moderated by the rise of sea level and decrease in land area (especially on the emergent continental shelves) associated with fast spreading rates (Pitman, 1978), a lthough perhaps with a time lag (Heller and Angevine, 1985). In addition, an increase in weathering rates on land may lead to greater nutrient supply and organic carb o n b urial rates,


66 which would tend to draw down atmospheric C02 via its consumption during photosynthesis. The weathering of organic carbon produces C02 and this may tend to offset the depletion due to weathering of other crustal materials. It becomes apparent that at this level of complexity intuition may fail, so numerical box models have been developed to dea l quantitatively with the system of fluxes (e.g. Berner et al., 1983; Lasaga et al. 1985) In the next section some results from an example of this type of model will be presented. The Present-Day System Figure 16 represents the presentday configuration of the global sedimentary, geochemical system The design and most of the details are identical to the version of BLAG presented in Lasaga et al. ( 1 985) and the reader is referred to that paper for an in-depth discussion of the assignment of sizes and fluxes to the various reservoirs. The changes to be noted here are i) the addition of the fluxes to and from the atmospheric 02 and sedimentary pyrite reservoirs due to sulfate reduction, pyrite production and weathering, and ii) the removal of the fluxes to and from the pyrite reservoir due to metamorphism and volcanic-seawater interactions (see justification below). Oxygen Levels And Weathering The functional relationship between atmos pheric 02 levels and oxidation rates of reduced sedimentary constituents during weathering has been discussed in Chapter 1 In that chapter arguments were presented that supported the assumption that there is a direct correspondence between P02 and oxidation rates. It then seems


Figure 16. Box model of the present-day, global, long-term geochemical cycle, adapted from Lasaga et al. 1985. Fluxes in 1018 moles/106 yr, reservoir sizes in 1018 moles


3 0 COt I 2 .90 COt Mtomorphitm Molamarphl o m 3 8 Ot 3 .80 CO t Oz weathetinQ C02 C-Burial Org C WEATH E R I N G ro.;e 38 3 8 Oz 0 .055 1250 02 c Burial 3 .80 COt Woalhorinq 3 .96 COt I l W oalhoring 02 0 .,1 so. 1 Pyrit e Roducllan 7 .84 co.. 250 17.38 wcalhorlng 118. 4 HCO, 0.12 504 I l 2 .1 0 MQ 18. 4 ca "+ WoathorlnQ Oceans ,.recipi tat ton Dolomite 2 .10 Ca 16.14 Hco, Calcite Mg Co so4 HC03 weothetlnv 1000 0 .12 so. 8 .30 Co 3000 ...___ 8 .16 HCOs 75 6 14 40 2 8 0 .23 so. ;; .. 0> 0 0 D J 0 "c: a :i:; 0 X u "' N N ., 0" 0 1 .02 Co SQ, .. ... 0 .. c .. ,; ; eli ci woalnorong CoS04 s ., Q 1 .02 Co 504 > Proci plio lion 250 .. Ca M etomorphl m ' Mg Co-Mg S i I icotes 2 .90 ca M otomorphiam 0 .16 so Wcothering 0 .23 so t Woathorlnv L_ ___ 11.48 COt Woothorlnq f+-r-I I "' CX>


69 to that the of weathering of and organic be as: F = k M(py) w,py w,py Fworgc = M(orgc) ( 19) (20) kw,py = k0w,py fa(land fb(C0 2 ) fc(02 ) (21) = fa(land fb(C0 2 ) fc(02 ) (22) and F x is the flux of x in 10 18 moles my, k is the w, w,x constant in my-1 M(x) is the nBss of x in 1018 moles, f a is the land area and fb is the (see BLAG; Lasaga et al., 1985). The factor 02, fc, is simply the of M(02)/M0(0 2 ) M0(0 2 ) is 38 x 1018 moles, the present-day value. If the and written as Ff,orgc and Ff,py' the of change of the 0 2 is: dM(02)/dt = + 15/8 Ff,py-15/ 8 Fw,py (23) the 15/8 the of the te and reactions. And Isotope Equations The gleaned the isotopic of and sulfur can be used to calculate Ff Ff py' and the oceanic mass of sulfate, M(SO .. ) based on the of conservation of total mass and isotopic composition. To simplify the of the equations the following notation will be used: Mi will denote the mass o f the i th with i=1 denoting the pyrite S 2 the


70 2-caso .. 3 the ocean so.. 4 the ocean HC03-, 5 the CH20, 6 the CaC03 and 7 the Mgca(C03) 2 reservoirs. The standardized ratios of heavy to light isotopes, 6 3'*S and 613C, are then expressed as 6i. The reservoirs are assumed to be homogeneous with respect to their isotopic oomposition. The principle of conservation of mass can be expressed as: Ml + M2 + M 3 = MS(total) M .. + Ms + M6 + 2 M7 = MC(total) and that of isotopic composition as: 61M1 + 62M2 + 63M3 6SMS(total) 6 .. M .. + 65M5 + 66M6 + 2 67M7 = 6CMC(total) (24) (25) (26) (27) where all the terms on the right are constants with respect to time, so: (28) If the flux of material from reservoir i to reservoir j is written Fij' equations 28 and 29 can be rearranged to: M3 d63/dt + 63(Fl3+F23-F31-F32) = -(F31(63-Es) Fl36l) -(F3263 -F2362) (30) where Es is the isotopic fractionation factor for pyrite production (no appreciable fractionation occurs during gypsum precipitation), and M .. d6 .. 1dt + 6 .. (F5 .. +F6 .. +2F7 .. -F .. 5-F .. 6 ) = -(F .. s(6 .. -Ec) F5 .. 65 ) -(F .. s6 .. -Fs .. 6s)-(-F7 .. 67) (31) where Ec is the isotopic fractionation factor for photosynthesis (no appreciable fractionation occurs during carbonate precipitation). Upon rearrangement of equations 30 and 31, expressions can be written for the rate of formation of pyrite ( F 31 =Ff ) and burial of organic carbon ( ,py (F F ) '*5 f,orgc


1/Es {M3 do3/dt Fl3Col-o3) F23(o 2-o3)} 1/Ec 71 (32) (33) Note that i) d6 3/dt, 63 and are all given functions of time; ii) and include the fluxes of C02 due to metamorphism of calcite and dolomite ; and iii) F H is also actually a flux of CO2 to the atmosphere rather than directly to the ocean (reservoir 4). The exchange of carbon between the atmosphere and ocean is instantaneous in the time frame of this model, so it is assumed here that the isotopic flux due to these processes is directly to the ocean; no atmospheric isotope balance is calculated. Gypsum (and Anhydrite) Deposition The isotope equations for S contain an excess of unknowns. In earlier papers closure has been achieved by either assuming constant ocean sulfate mass (e.g. Garrels and Lerman, 1981, 1984; Berner and Raiswell, 1983; Lasaga et al., 1985) or by assuming to be a known function of time (Lasaga et al., 1985). A third alternative is presented here: to specify a function f o r the depositional rate of as a function of geologic time, based o n the known abundance of preserved evaporites through time (Helser 1984) and the constraint that total ocean saturation with respect to gypsum cannot be exceeded for any length of time (Holland, 1972) This method seems reasonable in view of the episodic nature of evaporite formation, which is dependent on a variety of climati c geographic, and oceanographic conditions (e.g. Holser, 1984). Holser ( 1984) shows that the only significant accumulation of gypsum during the last 100 my occurred during the


72 Miocene, which time 11 x 1018 moles of deposited. The data of Ronov (1982) which also include disseminated gypsum document a Eocene peak as well. To evaluate the sensitivity of the model to the of the gypsum function chosen two cases tested. The specifies that the of gypsum has been constant the last 100 m.y., at a value of 1.0 x 1018 moles/my. The second, a one, specifies that the was low, 0 .5 x 1018 moles/my, 100 mybp to 20 mybp, then to 3.0 x 1018 moles/my 10 my, at which time it fell again to the low value the last 10 my. These values also chosen so that the chemical composition of the ocean less within the limits set by Holland ( 1972, 1984). Calcite Depositional Rate Function The flux of calcite the ocean has been modeled such that the ocean with to caco 3 This has been achieved by relating this flux to ocean to the following et al., 1983): Fcc= the constant is defined as: Keq = [M(Ca)eqM 2(HC03)eq]/M(C02)eq When the ocean is in with CaC03: ( 34) (35) (36) and F is If M(Ca) M(HC03 ) to in the ocean cc without a in M(C02), Fcc would to oceanic


73 This feedback relationship appears well constructed yet there is an aspect of it that runs contrary to intuition. Most empirical rate laws of the kinetics of carbonate dissolution and precipitation include a saturation-state term (U) which is the ratio of the concentration product (CP) to Keq When the species involved are in equilibrium CP=Keq and 0=1. If the system becomes supersaturated (U>1) the rate of precipitation increases and n returns to unity. Similarly as n falls below unity the rate of dissolution increases and Table 3 explores the relationship between n and F for two roodel cc runs: the roodified BLAG run of Lasaga et al. (1985) and the sensitivity run to be described below in which the mean isotopic value of the carbonate reservoirs is chosen to be 1 5 I 0 0 and the depositional rate of gypsum is allowed to vary with time. Note that n does not deviate greatly from unity; considering the extremely short residence times involved, the functional relationship performs as expected. The unexpected result, however, is the antipathetic relationship between n and Fcc; the former increases yet the latter decreases over the course of the 100 my runs. The way this comes about is revealed if equation 34 is rewritten as: (37) where (38) According to equation 37, Fcc can indeed decrease as CP increases if M(C02 ) falls proportionally more rapidly than [CP-K q] rises. e There are at least two alternative flux equations that avoid this difficulty. One is a simple modification of equation 34: (39)


74 Table 3. Model calculations of Galcium Carbonate Saturation Age (my) 100 80 60 40 20 0 CP [M ( Ga) M 2 ( HCO 3 ) ] M(C02 ) LABEGA KUMP 1704 1798 1676 1821 2004 1912 1839 1970 2046 2031 2133 1921 LABEGA-------Lasaga et al., 1983 0 CP/Keq LABEGA KUMP 0.99 1.04 0:91 1:06 1:16 1.11 1.07 1:14 1.19 1.18 1.24 1.15 Fcc (1018 mol/106 yr) LABEGA KUMP 26 20 23 19 18 18 20 14 16 15 17 19 KUMP----------This chapter's run with variable Ff and a mean o13C of ,gy 1.5 /00 for the carbonate reservoirs Keq 1723.3


75 The primary objection to this expression and to equation 34 as well is the necessity of specifying two parameters. BLAG used the modern-day Fcc and a clever line of reasoning based on the turnover time of the ocean to approximate Keq and kpr The second alternative avoids the specification of rate and equilibrium constants altogether. It demands a more restrictive assumption abouth the chemical composition of the ocean-atmosphere system, in particular, that it absolutely remains in equilibrium with CaC03 over the time scales modeled. Thus: where the prime designates the time derivative. By the product and quotient rules of differentiation equation 40 becomes: Now let 2M(Ca)M(C02)M'(HC0 3 ) + M(HC03)M(C02)M'(Ca)M(Ca)M(HC03 )M'(C02 ) = 0 M (HC03 ) = M'(HC03 ) + 2Fcc M ( Ca) = M I ( Ca) + Fcc M (C02 ) = M'(C02 ) -F cc (40a) (40b) (40c) (40d) then by substitution * 2M(Ca)M(C02)[M (HC03)-2Fcc] + M(HC03)M(C02)[M (Ca)-Fcc]M(Ca)M(HC03 )[M*(C02)+Fcc] = 0 (40e) designates the derivative which is based on all fluxes except where Fcc Upon rearrangement * F = [2M(Ca)M (HC03 ) + M(HC03)M (Ca) cc {M(Ca)M(HC03)1M(C02)}M (C02)] I [4M(Ca) + M(HC03 ) + M(Ca)M(HC03)/M(C02)] ( 41 ) The third term in the denominator is dominant, so an approximation of


76 equation 41 can be written as: * Fcc = M(C02)[ 2M (HC03)1M(HC03) + M (Ga)/M(Ga) M (C02)/M(C02)] (41a) Thus the calcite burial flux will be large when M(C02 ) is large, when the residence time of the oceanic ca and HC03 reservoirs is short, and when that of the atmospheric C02 reservoir is long. The latter approach differs from the kinetic treatment which is the foundation of BLAG and its modifications, and so may be unappealing to some modelers. Some may question whether it is justifiable to so severely constrain the system. Two arguments are put forth in defense of this approach: 1) The present-day ocean is in equilibrium with respect to calcite. This conclusion is based on a simple vertical integration of the saturation state of the world mean ocean that uses the summary data of the GEOSECS program in Takahashi et al. (1980); 2) The vertical structure of ocean saturation, with supersaturated surface waters and undersaturated bottom waters, provides an ideal mechanism for maintaining ocean saturation. The response time of the ocean-atmosphere system to a perturbation from equilibrium should be on the order of several turnover times of the ocean (thousands of years); The BLAG representation (equation 34) is unable to accomplish this. For these reasons it may be preferable to use equation 41 to calculate the depositional rate of calcite for integrations of cycling IOOdels over millions of years. Shorter-term models should perhaps be constrained by this assumption as well; flux relations should be


77 constructed that will maintain ocean saturation over time scales greater than a few thousand years. Equation 34 is used for the first set of sensi ti vi ty runs The second set of sensitivity runs and all subsequent runs use equation 41. General Kinetic Equati ons And The Operation Of The Model The set of kinetic equations used here is similar to those of Lasaga et al. (1985) with the exception of the modifications discussed above, and these two simplifications: 1 ) the thermal decomposition of pyrite and organic carbon during subduction is assumed to be negligible because of the low content of organic carbon and pyrite sulfur in deep-sea sediments; 2) the flux of pyrite due to the reduction of sulfate as seawater circulates through hydrothermal systems is assumed to be negligible (see discussion in Holser et al., 1979, and Holser et al., 1984). There are seventeen differential equations in time governing the evolution of the sedimentary, oceanic and atmospheric reservoirs (Table 4); the notation used is nearly identical to that used in Lasaga et al. (1985). The integration in time is carried out using the implicit, multi value, numerical method of Gear ( 1971). The min program the differential equation subroutine, and the initiation program are presented in the Appendix. Initial Conditions (Subroutine INITSS) These equations must be numerically integrated forward in time (Kasting 1984), so initial values must be chosen for the reservoirs and their isotopic compositions at 100 rnybp such that the present-day conditions are attained at the end of the run. For the large,


Table 4. General Kinetic Equations M'(dol) = -[kw,dol + km,dol]M(dol) kwo,pyM(py) fdol M'(cc) = -[k + k ]M(cc) 2 k M(py)f w,cc m,cc wo,py cc + F + 2Ff 00 ,w M'(CaSi) = km,ccM(cc) + km,dolM(dol)kw,CasiM(CaSi) kw,MgsiM(MgSi)kwo,py M(py)fcasi M'(MgSi) km,dolM(dol) + kv-swMMg-kw,MgSi M(MgSi) kwo, pyM(py)fMgSi M'(orgC) = Ff,orgCkwo,orgcM(orgC) M'(py) = Ff,py-kwo,pyM(py) M'(gy) = Ff,gykw,gyM (gy) M'(0 2 ) = M'(orgC) + 15/8M'(py) M'(Mg) kw,dolM(dol) + kw,MgSi M(MgSi) + kwo,pyM(py)[fdol+fMgSi] -kv-swMMg M'(Ca) = kw,dolM(dol) + kw,cc M(cc) + kw,CaSi M(CaSi) + k M(Mg)+ k M(gy) Ff 2 Ff v-sw w,gy ,gy ,py + kwo,pyM(py)[fdol+ 2 fcc+fcasi] Fcc 78 (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) M'(S0 4)= kw,gyM(gy) + kwo,pyM(py) Ff,gy-Ff,py (k) M'(Hco3)= + 2 kw,cc M(cc) + 2 kw,CaSi M(CaSi) + 2 kw,MgSi M(MgSi) + 2kwo,pyM(py)[fcc+fdol] 2F 2 F f,py cc (1) 2[(i) + (j) -(k)] {Charge Balance}


79 Table 4 (cont'd) + kwo,orgcM(orgC) + Fcc -Ff,orgC2kw,CaSi M(GaSi) 2kw,MgSi M(MgSi) (m) o34S = F [o34S E o34S J 1 M(py) (n) py f,py oce s py o34S = F [o34S o34SgyJ 1 M(gy) (o) gy f,gy oce (p) (q) o13Cdol' 0 {assuming no dolomite formation for last 100 my} (r) where M(x) is the size of the x reservoir, M'(x) is dM(x)ldt, fx is the fraction of the total sulfuric acid flux used to weather the x reservoir as defined in Lasaga et al. (1985), and F c c is either defined by equation 34 or equation 41 in the text kw,x = kow,xfA(t)fa(C02) [land area and co 2 corrected weathering rate constant] kwo,x = k0wo,xfA(t)fa(C02)fc(02) (s) [kw with oxygen correction] (t) ,x km,x 2 kom,xfsR(t) [metamorphism rate constant with spreading rate correction] (u) kv-sw = k0v-swfsR(t) [spreading rate corrected volc.-seawater reaction rate constant] (v)


80 sedimentary reservoirs that have turnover times that are long with respect to the length of the integration, the initial conditions are easily adjusted to obtain the present-day solutions (the so-called "shooting" method) For the oceanic and atmospheric reservoirs, however, which turn over many times during the course of the integration, there are an indefinite number of combinations of initial values that will give the present-day reservoir sizes. Following the reasoning of Kasting (1985) the additional boundary condition that the fastest cycling reservoirs, oceanic ca2+ and HC03 and atmospheric C02 are at quasi steady-state at 100 mybp, is imposed. In addition, given the initial sizes of the sedimentary reservoirs and the constraint of conservation of mass one may calculate the initial masses of 02 in the atmosphere, M(02 ) and sulfate in the ocean, M(02 ) = M0(02 ) + (M(orgC)-M0(orgC)) + 15/ 8 (M(py)-M0(py)) (42) = ES -M(py) -M(gyp) (43) It is anticipated that the isotopic composition of the gypsum reservoir will vary little during the course of the run because of the predominance of weathering over deposition; thus it is assigned its presumed present-day value of 20/00 (Helser, 1984) For the oxidized carbon reservoirs, the choice is especially critical because of the sensitivity of the model to even small uncertainties in our knowledge of the average isotopic composition of the present-day calcite and dolomite reservoirs. The simplification was made that at 100 mybp, the isotopic values of the calcite and dolomite reservoirs were identical. To test the sensitivity of the model to this value, three runs were performed, one with o 6=o7=1.3/ 00, another with 06=07=1.5/ oo' and a third with o 6=o 7= 1 7 I o o


81 '!he necessity of charge balance in the ocean, and the empirical relationship between weathering rate and M(C02 ) derived by Berner et al. (1983) provide the last two equations needed to define the initial conditions. Note that it is not required that or dM(Mg)/dt be zero at the start of the run. These reservoirs turn over more slowly than the other oceanic reservoirs, with residence times of 26 my and 15 2+ -my, respectively, in contrast to 0.7 my for Ca 0 .15 my for HC03 and 2400 yr for atmospheric C02 However, charge balance requires that at t=100 mybp these derivatives be equivalent. Sensitivity Runs In total, six runs were executed for three values of 6 1 3C b and car for two gypsum depositional rate functions. The results are presented in Figures 17 through 29. In addition 19 runs were performed to test the sensitivity of the model to its rate constants, fractionation factors, and weathering-rate correction factors. The results of these runs are presented in Figure 30. Results and Discussion An aspect of the continual refinement of the BLAG model is the difficulty involved in making specific comparisons between the results of the model runs presented here and those in Berner et al. ( 1983), Kasting ( 1 985) and Lasaga et al. ( 1985), because of differences in forcing functions, rate constants, and components considered In this analysis one is most concerned with the sensitivity of the total system to adjustments of the redox subsystem and to the level of uncertainty associated with various parameters including rate constants,


82 fractionation factors, and weathering rate correction factors. Gypsum Burial and Carbon Isotope Sensitivity The first analysis concerns the sensi ti vi ty of the total system to two variables: the imposed gypsum depositional rate function and the assumed initial c13C of the carbonate (calcite and dolomite) reservoirs. The results may be grouped into four categories based on their sensitivities to the parameters varied. First are those which were most sensitive to the form of the imposed gypsum depositional rate function. These include the reservoir sizes of sedimentary pyrite (Figure 17) and gypsum (Figure 18) sulfur, and of oceanic sulfate (Figure 19) and calcium (Figure 20). Second are those that were especially sensitive to the initial value chosen for the isotopic composition of the c arbonate reservoirs. These include the sedimentary organic carbon reservoir size (Figure 21), the burial rates of organic carbon (Figure 22) and, somewhat surprisingly, of pyrite sulfur (Figure 23) Third are those which were sensitive to both of these factors, and include the oceanic reservoir size of magnesium ( Figure 24) and the amount of atnnspheric oxygen (Figure 25) The fourth group includes those results that were relatively insensitive to the conditions varied, namely, the sedimentary reservoir sizes of calcite and dolomite (Figure 26) the burial rate of calcite (Figure 27 ) the oceanic HCO 3 (Figure 28) and, with a few exceptions, the atmospheric C02 reservoir (Figure 29) Sensitivity to Gypsum Depositional Rate (Figures 17 to 20) Under the condition of constant gypsum deposition, the nndel predicts slow, constant diminution of the gypsum reservoir, with a short growth period at about 15 mybp, that is compensated for by an increase in oceanic


Figure 17. The model sensi ti vi ty of the pyrite reservoir size to the variation in mean o13C of the carbonate reservoir and to the form of the gypsum burial rate equation.

PAGE 100

" (/) w ..J 0 :E .. 0 .... v Ill ,.. Q. :E 100 SEDIMENTARY PYRITE SULFUR RESERVOIR eo 60 AGE <108 YR> 40 CYP. OEPOS. RAT < FF.CYP) FIXEO VARIED t .SO 1!11!11!1 ) I >( Me ... i 1.70 HZ ....... 20 0 co .l::'

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Figure 18. The model sensitivity of the gypsum reservoir size to the variation in mean o13C of the carbonate reservoir and to the form of the gypsum burial rate equation

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" Ul w _J 0 :t: 0 ..... 'V :t: 240 SEDIMENTARY GYPSUM RESERVOIR :a 1. 30 I i .. i 1.70 CYP. DEPOS. RAT < FF. CYP > FIX VARIED 1!11!11!1 Y-'( 2-H 100 80 60 40 20 0 AGE <1011 YR> co 0\

PAGE 103

Figure 19. The model sensitivity of the oceanic sulfate reservoir size to the variation in mean o13C of the carbonate reservoir and to the form of the gypsum burial rate equation.

PAGE 104

,... Ill w ..J 0 0 ..... v 1 N 20r I I 100 80 OCEANIC SULFATE RESERVOIR I I 60 AGE GYP. OP09 RATE < FF. GYP ) FJXED VARIED ls.SD I >aa< C9el!l ) t.50 I (Mf) .. i I. 70 I 2!i!i': ..... L I 40 20 0 <10 YR> l co co

PAGE 105

Figure 20. The model sensitivity of the oceanic calcium reservoir size to the variation in mean o13C of the carbonate reservoir and to the fom of the gypsum burial rate equation.

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....... ...... ::>a z.....,.> W_JW U<(J) ouw a:: "' ,_ I I l < Cl: i:; > .;. II. I J m iO: u 5I Q . --t.P 0 N 0 0 <0 0 a:l 0 N etO I> 90 ,.... a:: >-., 0 ..... v w <

PAGE 107

91 sulfate mass from 100 mybp to about 45 mybp, and then by growth of the pyrite reservoir with a slight drop in the oceanic sulfate reservoir until 0 mybp. These patterns are nicely mimicked by the runs under the condition of low depositional rates of gypsum for most of the interval, and high rates for the period from 20 mybp to 10 mybp. Again, the gypsum reservoir diminishes, at a quicker rate however, and as it does, sulfate accumulates in the ocean. At 20 mybp, the gypsum reservoir experiences rapid growth at the expense of the oceanic sulfate reservoir; the effect on the pyrite reservoir is not great, for its growth is determined by the isotope equations. The results for oceanic calcium parallel those for oceanic sulfate, indicating that gypsum deposition is an important sink for calcium. The lack of convergence to the present-day value of 1 4 x 10 1 8 roles of oceanic calcium is a reflection of its additional sensitivity to the operation of the carbon cycle; this will be discussed below. The major effect of differences in the specified gypsum depositional rate function appear in the partioning of oxidized sulfur between its two reservoirs, gypsum and oceanic sulfate. Bec ause gypsum is deposited with virtually the same sulfur isotopic ratio a s seawater sulfate, this partitioning is effectively transparent to the isotope balance equations. Thus, any constraints imposed by these equations must be satisfied by changes in reduced-sulfur cycling; the pyrite reservoir then shows little sensitivity to the imposed gypsum depositional rate function. Sensitivity to Carbonate Isotopic (Figures 21 to 23). The sensitivity of the model to the initial isotopic value of the carbonate reservoir (which actually changes little during the course of the run)

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Figure 21. The model sensitivity of the organic carbon reservoir size to the variation in mean o13C of the carbonate reservoir and to the form of the gypsum burial rate equation.

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"' (./) w ..J 0 X .. 0 ..... v u 128 '8 1 .90 I l SO ..!" .. SEDIMENTARY ORGANIC CARBON RESERVOIR CYP. Da'OS. RAT ( FF. CYP ) F1XD VARIED I >t*K l!H9I!I I 'fJ( \Me I i t. 10 I Hi: ..... 1 00 80 60 40 20 0 AGE \0 w

PAGE 110

Figure 22. The model sensitivity of the burial rate of CH20 to the variation in mean o13C of the carbonate reservoir and to the form of the gypsum burial rate equation.

PAGE 111

95 w A ... I I 1 < u> ... ..: 0 I l ... "' X ... u i Sl 0 .... .: .: .: (10 / a > IAIV::I::J t'"f' 0 ., "' a:: >Cl 0 .... v UJ z t..:) ow < (Df-0 10 u --' U< t-1 t-1 <:::J lJ(D 0 e01/S310W etOD J

PAGE 112

Figure 23. The model sensitivity of the burial rate of pyrite S to the variation in mean o13C of the carbonate reservoir and to the form of the gypsum burial rate equation.

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.. a I I ) r; > l!! ... c I l "' "' 0 X N 0:. ,_ ... u Iii i! c ... .: .: ..: / o> IIIIV:l::IE t t 0 0:: :JW 0 LL.,_ co _j< :JO:: (f) _J W< ................ -a:: O:::J >-m Q_ 0 CD N N ..: -a01/S3lOH etOD 97 0: >II 0 ...... '-J w (.j <

PAGE 114

98 is predictable from the expressions for the rate of burial of pyrite sulfur and organic carbon given in equations 32 and 33. In the model calculations, the magnitude of these fluxes is a function of the difference in isotopic compositon between the sedimentary and the oceanic reservoirs. For example, when o13Ccalcite is more positive than o 1 3C F is diminished, and vice versa. This feedback ocean' f ,org c rrechanism drives the nx:>del towards isotopic steady state, in which 1 3C o 13C = o 1 3C + co (see Chapter 1) F1' gure 22 v calcite ocean org c c..c shows that Y-lhen the initial carbonate isotopic value is more positive ( 1. 7 I o 0 ) the burial rate of organic carbon decreases throughout the run, whereas when it is less positive (1.3/00) it increases throughout the run. From Figure 22 it appears that the average o 13Cocean must be near 1.6/00 for the last 100 my, because this would represent the value of the carbonate reservoirs for Y-lhich the carbon cycle would operate near isotopic equilibrium. Indeed, the average oceanic carbon isotopic value for the last 100 ITrf is J .575 I 0 0 The reason for the high. sensitivity of the pyrite burial rate to o13C b is less obvious than that of organic carbon, yet it is revealed car by a close inspection of equation 32. The link is indirect, and involves the effect of atmospheric 02 level on weathering. In general, high organic carbon burial rates indicate high oxygen levels (see below) which increase the weathering rates of organic carbon and pyrite sulfur and F13 in equations 32 and 33). An increase in F13 tends to lead to a n increase in F31 (Ff,py) by equation 32. (Note that o1-o3 is a negative number.) The shared influence on, and response to, atmospheric 02 is the effective, long-term couple between the carbon and sulfur cycles. Because the fluxes to and from the 02 reservoir as a result of

PAGE 115

99 the operation of the C cycle are normally much larger than those of the S cycle, 02 levels, and subsequently pyrite burial rates, track long-term changes in the burial rate of organic carbon In detail, however, there are several intervals, for example the period from 96 mybp to 88 mybp, during which Ff and Ff take . ,org c ,py opposite excursions. nie: for these occurrences lies in an even rrore indirect relationship Ff ,py' atrrospheric C02 and 02 levels, and weathering rates. A sudded decrease in Ff leads to an ,orgc equally sudden increase in C02 according to Table 4, equation m The decrease of the 02 reservoir is buffered due to its large size. The effect on the sulfur cycle a sudden, large increase in weathering -rate, despite the slight opposing effect of the drop in 02 which leads to a sudden increase in Ff according to equation 32. ,py Thus, the long-term coupling between the carbon and sulfur cycles in this rrodel involves the atmospheric 02 reservoir, which is large and responds slowly to changes in fluxes to and from it. This coupling leads to a positive relationship between Ff,py and Ff,orgc On the shorter term fluxtuations in organic carbon burial rates are transmitted quickly to the sulfur cycle via the quick-to-respond atmospheric C02 reservoir. This coupling leads to a short-term, inverse relationship between F f, PY and F orgc. Sensitivity to Both Variables (Figures 24 and 25). There are a few variables which appear to be nearly equally sensitive to both the choice of the gypsum depositional rate and the initial 013Ccarb These include the oceanic reservoir of Mg2+ and the atmospheric reservoir of 02 Both of these reservoirs are intimately affected by variations in the carbon and sulfur cycles (Table 4, equations h and i) so the sensitivities are

PAGE 116

Figure 24. The model sensitivity of the oceanic Mg reservoir size to the variation in mean o13C of the carbonate reservoir and to the form of the gypsum burial rate equation.

PAGE 117

I!! s A' ,. c u > ai L&. a .., 0: ,. L&. u 2:0::: u:::::> ....... ............ a Z(f)> ., a -v w <..:) <

PAGE 118

Figure 25. The model sensitivity of the atmospheric 02 reservoir size to the variation in mean o13C of the carbonate reservoir and to the form of the gypsum burial rate equation.

PAGE 119

"' lf) w -' 0 !!! 0 ... 'J 80r-------.-------.-------.-------.-------.-------.-------.-------.-------.-------, ATMOSPHERIC OXYGEN RESERVOIR 11 1.30 I.SO ..t" .. i 1.70 CYP. DEPOS. ( FF, CYP > FIX YAIUEO IHII!I y..>p( tMf) 2-R.,i. 00 0 AGE 0 w

PAGE 120

104 not unexpected. The shape of the Mg2+ curve is influenced strongly by the C02 curve (Figure 29), indicating the importance of the weathering flux of Mg2+ (a function of PC02 ) to the overall balance of its oceanic reservoir. The inverse relationship between C02 and 02 reflects the tendency for the C02 reservoir to shrink and the 02 reservoir to grow as the organic carbon reservoir grows Insensitivity to Both Variables (Figures 26 to 29) Finally consider the relative insensitivity of the sedimentary reservoirs of calcite and dolomite, the oceanic reservoir of HCO 3-, the atroc>spheric reservoir of C02 and the burial rate of CaC03 to the varied conditions of the six roc>del runs. The continual transfer of carbon from the dolomite to the calcite reservoir is required by the specification that no dolomite be deposited over the course of the run. The dolom ite reservoir continually erodes, and as it does, the calcite reservoir must grow as it is the only other large reservoir for inorganic ca rb on Its growth is regulated by the depositional rate function for CaC03 which is designed to keep the ocean near saturation with respect to CaC03 The C02 and HC03 reservoirs are perhaps surprisingly insensitive to the variations imposed on the model considering their Slll3.ll sizes and rapid turnovers. As demonstrated by Kasting ( 1984) these features are what confine C02 and HC03 levels to near their modelled equilibrium values. At equilibrium the C02 level is prilll3.rily dependent on the reservoir sizes of calcite and dolomite, which have been shown to be complementary, the ratio of the correction factors f sr/f a, which decreases throughout the run, and the burial rate of organic carbon The latter influence, which was not part of some of the earlier models ( Berner et al., 1983; Kasting, 1985) accounts for the increased

PAGE 121

Figure 26. The model sensitivity of the calcite and dolomite reservoir sizes to the variation in mean o 1 3C of the carbonate reservoir and to the form of the gypsum burial rate equation.

PAGE 122

" u Ul 2BOOJ.W _J 0 ::l: 0 ..... V u u ::l: ... ... ; ::l: 18001 I 100 I 80 SEDIMENTARY DOLOMITE RESERVOIR CYP. DEPOS. RATE < FF.CYP) FIXED VARIED :S 1 3D I >a++< I!II!H!J 1 .so I >t' cY "' (9Ml 1.10 ..... L 60 AGE 40 SEDIMENTARY CALCITE RESERVOIR 20 0 0 0\

PAGE 123

Figure 27. The model sensitivity of the burial rate of calcite to the variation in mean 613C of the carbonate reservoir and to the form of the gypsum burial rate equation

PAGE 124

"' ... ... I < Q: ...: l!! ... Q I .... "' )( 0:. ... u Iii ..: {"' /o) I 1 l Q ..... ..: ..: tiiP w I-< zw 01-m < Ct:Ct: < U_j < ::E::Jet: -::J urn _j < u 0 a01153lOW etOD II 0 ... v w l:l < 108

PAGE 125

28. The model sensitivity of the oceanic bicarbonate reservoir to the variation in mean. o13C of the carbonate reservoir and to the form of the gypsum burial rate equation.

PAGE 126

0 "" Ill ... ... < II: o.CI: ... < u> &L ... c cL ... ... u w r--n:: ZO> I J l i Q .: .: t"'P etOD 0 0 ..,. 0 10 0 CD 0 110 "" Q: >II 0 v UJ t:l <

PAGE 127

Figure 29. The model sensitivity of the atmospheric C02 reservoir size to the variation in mean o13C of the carbonate reservoir and to the form of the gypsum burial rate equation.

PAGE 128

" (/) UJ .J a :: .. a '-' 8 :: o. I I ATMOSPHERIC GYP. DEPOS. RATE CARBON DIOXIDE ( FF,GYP) RESERVOIR FIXED YARlm I >aa< 1!!11!1 J t. so I 'f eee COl o. 2r-I i l. 10 I HZ .... o. 1 ____ _L ____ _L ____ _L ____ _j 100 80 60 40 20 0 AGE (lOll YR> -" _. 1\)

PAGE 129

113 variability of C02 levels relative to those calculated in the other rrodels, and the inability of the rrodel to generate the exact present oceanic and atmospheric conditions. The CaC03 burial rate is even less sensitive to the factors varied than are the variables which determine it, namely oceanic calcium, bicarbonate, and atrrospheric C02 This decreased sensi ti vi ty results from the roughly inverse relationship between M(Ca) and M(HC03 ) and the positive relationship between M(HC03 ) and M(C02); these relationships tend to offset any major influence on the carbonate depositional rate. Sensitivity to Other Model Parameters Several runs were performed to test t h e sensitivity of the calculated mass of atmospheric 02 to a level of uncertainty in various assumed parameters in the model. The results are presented in Figure 30. The calculation was insensitive to a +I1 O% variation in all of the weathering rate constants and in the land area and spreading rate correction factors; these runs ar-e plotted without labels in Figure 30 because of the modest variability shown. Oxygen levels wer-e much more sensitive to variation in c and s which were varied + / 5%. Of the two the carbon isotopic fr-actionation factor exerted the greater influence on 02 This was expected, as the dominant flux of 02 to the atmosphere is via organic carbon burial; F f ,orgC in this rrodel is dependent on c. The subsidiary oxygen flux due to pyrite burial is of course dependent on hence the decr-eased yet significant sensitivity s of the calculation to the sulfur isotopic fractionation factor. Or-ganic Car-bon Burial

PAGE 130

Figure 30. tvbdel sensitivity of atmospheric 02 to 10% variation in the weathering rate constants, land are and spreading rate correction factors (all of these plot in the thick inner band), and to 5% variation in Ec (outer pair of plots, +C and -C) and in (inner pair of plots, +Sand-S). s

PAGE 131

0 CD 0 CD 0 0 N 0 0 N ow CDC) < 0 00 0 115

PAGE 132

116 The burial rate of organic carbon over millions of years is essentially regulated by the rate of nutrient supply (primarily phosphorus) from rock weathering and the efficiency of utilization of these nutrients. The global depositional rate of organic carbon (CH20), designated as F c g, can be resolved into the component supplied by terrestrial CH20 production, Fct' which may be buried on land or beneath the sea, and its marine component, Fern: F g = F t + F m (44) c c c The global Ji'losphorus weathering-supply rate, F P, and its rerroval rate with CH2 0 burial can be written: where Fp = Fct(P/C)org,t + Fcm(P/C)org,m (P/C)org,t = phosphorus/carbon ratio in buried terrestrial organic matter, and (P/C)org,m = phosphorus/carbon ratio in buried marine organic matter. (45) Since the terrestrial phosphorus to carbon ratio is much smaller than the marine ratio (cf. Sholkovitz, 1973; Froelich et al., 1982), an increase in Fe t relative to Fern under constant nutrient supply would lead to an increase in Fcg according to equations 44 and 45. Conversely, an increase in the removal of phosphorus during marine burial, F c m, could well result in a decrease in F c t and F c g under constant Fp. Only with an increase in Fp could an increase in Fern lead to an increase in Fcg It is suggested then that a significant part of the variation in the global depositional rate of organic carbon, and thus in the carbon isotopic compositio n of the ocean, is due to change in the ratio of the supply of terrestrial to marine organic matter to sediments. If this is

PAGE 133

117 so one should be able to observe two phenomena in the geologic 1 ) a between the isotopic and the of to sediment deposition, and 2) a lack of to the of land plants (R.M. communication, 1986). 31 plots both the o13C age (Lindh, 1983) and the the (Ronov, 1982). Both of the phenomena above can be observed in this Which suggests that indeed the global depositional of is by the source of organic with its C/P utilizes the available efficiently, thus allowing a global flux of in the of CH20 may then be expected to lead to fluctuations in the of supply of 02 to the atrosphere. These in 02 possibly confined within limits by at least two acting on time scales. On (less than million time scales, a negative feedback system exists that includes the 02 level, organic decay, Watson et al., 1978) and (Holland, 1978). An increase in CH20 burial for whatever reason leads to an increase in atmospheric and oceanic 02 levels. Respiration and decay increase in to increased 02 as does the probability of fire; hence the burial rate of organic carbon decreases, and 02 levels decrease. A similar line of reasoning applies to the response of 02 to a decrease in carbon burial. On longer time scales (millions of years) 0 2 levels have been regulated by both the tendency towards steady state due to the coupling

PAGE 134

Figure 31. Demonstrated relationship between o13C (+; Lindh, 1983) and the ratio of the volumes of terrigenous and marine sediment deposited in a given period (bars; Ronov, 1982).

PAGE 135

0 tn N .-4 V TERR/V MAR 0 l{) 0 .-4 0 00 0 0:: ,..---_..---to>o ..._ _____ -4('1)(0 0 ..... v 0 ow 0 0 IJ) 0 0 (() < 119

PAGE 136

120 of the C and S cycles (Chapter' 1) and the alternation of the global depositional envit'onment ft'om the tet't'estr'ial, to the not'mal mat'ine and euxinic modes tht'oughout geologic time (Bernet' and Raiswell, 1983). Changes in 02 level may pr'imat'ily have occut't'ed dut'ing not'mal mat'ine pet'iods; under:' euxinic Or' ter't'estt'ially-dominated conditions the cat'bon and sulfur' cycles may have been t'oughly compensatocy (see Chapter' 1). The ultimate factor' that detet'mines the global depositional envit'onment is likely tectonics, tht'ough its influence on sea level, on atmosphet'ic C02 and indit'ectly on weathet'ing t'ates and nutt'ient supply. Tentative Intet'pt'etations Of The Miocene Wot'ld Ft'om a global modeling pet'spective, the Neogene pr:'ovides an ideal set of conditions under:' which a model such as the BLAG extension desct'ibed het'e can be tested. Obset'vations and intet'pt'etations detailed above suggest that the Miocene was a pet'iod of high bUt'ial t'ates of ot'ganic cat' bon and pyt'i te sulfur', of high atrrosphet'ic 02 levels, and pet'haps of high C02 levels as well. An assessment of these conceptions of the Miocene wot'ld ca n be made ft'Om the model t'esults pr:'esented above. However', because of the possibility of high spt'eading t'ates in the Miocene, one final t'Un will be desct'ibed i n which the cut've of Kominz ( 1984) is used for' the spt'eading t'ate cot't'ection factor'. Figut'es 32 and 33 show the calculated but'ial t'ates of CH20 and FeS2 for' the last 100 my. These t'ates at'e cet'tainly higher:' in the eat'liet' Neogene than they at'e today and show distinct peaks in the Miocene. Eat'liet' Tet'tiat'y and Cr'etaceous events at'e however' admittedly mot' spectacular'. As a consequence of the high but'ial r'ates of reduced sediments 02

PAGE 137

Figure 32. Model run with Kominz ( 1984) spreading rate curve showing the ca lculated burial rate of organic C

PAGE 138

0 N ow col:) < a CD 0 122

PAGE 139

Figure 33. Model run with Kominz ( 1984) spreading rate curve showing the calculated burial rate of pyrite S

PAGE 140

0 0 (-JA e01/S910W st01) 0 N CD 0 ...-4 \J ow < 0 ro 124

PAGE 141

125 production was high in the Miocene, and the Miocene displays a Cenozoic peak in the atmospheric 0 2 mass (Figure 34). This result was shown by Shackleton ( 1985) as well. As a co2consuming process the increased burial rate of organic carbon tended to counteract the increased production of C02 due to the increased sea-floor spreading rate of the middle Miocene (Figure 35). An implication of low C02 is that weathering rates, 'Nhich were generally on the rise throughout much of the Cenozoic due to an increase in land area, may have been somewhat surpressed during much of t he Miocene. This is indicated by Figure 36, 'Nhich shows the weathering rate of the MgSi03 reservoir as a function of time. Because of the tremendous size of this reservoir it is virtually unaffected by fluxes to and from it, so that its weathering rate in the model is responsive only to land area and PC02 Thus Figure 36 provides a good measure of global trends in weathering rates. The predicted general increase in this rate over the last forty million years is substantia ted by the Sr isotope record (Figure 15F) which displays a similar trend. Oceanic pH The potential change in the global ocean pH is especially pertinent to this discussion in light of the increase in solubility of phosphorus at low pH. According to the empirical relationship of Atlas (1975) the solubility of Pin seawater nearly doubles a pH falls from 8 0 to 7 .5. The pH of the ocean c an be calculated by the BLAG rrodel using the reservoir contents of inorganic carbon acco rding to (Berner et al., 1983): (46)

PAGE 142

Figure 34. Model run with Kominz ( 1984) spreading rate curve showing the calculated level of atmospheric 02

PAGE 143

0 (Q 0 (T) 0 0 N ow cot:> < 0 m 127

PAGE 144

Figure 35. Model run with Kominz ( 1984) spreading rate curve showing the calculated level of atmospheric C02

PAGE 145

lf') (T) N Q 0 0 0 (Se 1 ow etO 1) 0 0 0 N w OL) CD< 0 (X) 0 0 129

PAGE 146

Figure 36. Model run with Kominz ( 1984) spreading rate curve showing the calculated weathering rate of of the MgSi03 reservoir.

PAGE 147

0 N ow < 0 CD 131

PAGE 148

132 The results are shown in Figure 37. The low global oceanic pH of the late Cretaceous and early Cenozoic would have supported twice the arrount of total P stored in the ocean today. As the pH of the ocean rose through the Paleogene its ability to store P decreased, perhaps leading to supersaturation and the eventual promotion of the precipitation of phoshorite minerals. The possible increase in pH during the Cenozoic may have accompanied other major changes in ocean chemistry. The apparent lower depositional rate of evaporites during the first forty million years of the Cenozoic would have reduced the effectiveness of the ocean in maintaining its salinity in the face of the continual supply of solutes from weathering and stream discharge; as a result the concentrations of Na, Cl, ca, and in the ocean and ocean salinity conceivably increased. What effect this change in ocean chemistry would have had on phosphorite solubility in the ocean has yet to be adequately modeled. The rough correspondence between periods of major evaporites (early cambrian, Perm:>-Triassic, Cretaceous Eocene, and Miocene; Holser, 1 984) and phosphorites (Cook and Shergold, 1984) suggests a causal link between the two. As the Neogene evaporites were deposited ocean salinity perhaps dropped, and the major ions assumed their present concentrations. Summary A discussion of the geological records of the C, S, Sr, and 0 isotopic composition of seawater, and of the changes of global spreading rate and eustatic sea level has revealed a number of interesting excursions centered on the period s of Neogene phosphogenesis. Interpretations based on these records should be made only after careful

PAGE 149

Figur'e 37. Model run with Kominz ( 1984) spreading rate curve showing the calculated oceanic pH.

PAGE 150

0 N ow cot:> < 0 00 134

PAGE 151

135 consideration of the interdependent causes of variat ion in the records. In general, m.urerical box rrodels are used to sort out the feedbacks involved and make calculations. A global sedimentary redox model has been developed and incorporated into the BLAG geochemical model. The model has been run for the last 100 my under a variety of initial conditions, flux rates, and parameter modifications to test its sensitivity to perturbation. The calculation of atmospheric 02 is especially sensitive to variations in parameters associated with the isotopic balance of the system. Nevertheless, all runs predict that the Miocene was a period of high burial rates of organic C and pyrite S and of levels of atmospheric oxygen higher and carbon dioxide lower than today. Phosphorus is an important player in the global geochemical cycle, yet it has not been in corpora ted in to comprehensive models of the exogenic system. The global depositional rate of CH20 is for the most part controlled by the supply of phosphorus and its distribution between terrestrial and marine ecosystems. High global burial rates are more likely to occu r when the majority of the organi c carbon i s synthesized on land, where C / P ratios are high. Only under extremely high supply rates of P to the sea will increased global burial rates of CH20 be due to marine deposition. The Neogene phosphogenic episode may have been promoted by a high mean oceanic pH developed over the course of the Cenozoic. Lower Tertiary pH's may have allowed the storage of nearly double the present oceanic mass of P. Generally low Tertiary global precipitation rates of evaporites may have led to the accumulation of Na, Cl Ca, and so .. in the ocean ; increasing concentrations of these solutes may have

PAGE 152

facilitated their rapid removal under appropriate geographical conditions during the Miocene. The link to phosphogenesis has not been determined.

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137 CHAPTER 3. THE GLOBAL IRON CYCLE The global cycle of iron, from its weathering from crustal rocks, to its transportation by rivers to the sea, deposition in oceanic sediments, diagenesis, deep burial, uplift and re-exposure to earth's surface conditions has been of great interest to geologists and geochemists for many years. Alth ough particular aspects of the cycle have been studied in great detail, a comprehensive overview of the entire cycle is needed before the iron cycle can be incorporated into the global rrodel. The aim of this chapter is to present such an overview The redox chemistry of iron determines to a large degree its cycling rates and pathways. The weathering of iron minerals is almost invariably associated with the oxidation of iron from a mixed ferrous/ferric state in rocks (c.f. C larke, 1924; Shaw, 1 956; Huber, 1958; Pettijohn, 1963; Wedepohl, 1978) to a largely ferric state in soils (c.f. Mohr and van Baren, 1954; Raussel-Colom et al., 1965; Ponnamperuma et al., 1967; Wildman et al., 1968; Drever, 1971a; Robert, 1971 ; Cecconi et al. 1975; Rozenson et al. 1980; Lindsay, 1983; Arduino et al., 198 4; Grieve, 1985). Stream transport of iron occurs almost entirely in the oxidized state (c.f. carroll, 1958; Coonley et al. 1971 ; d 'Angle jan and Sni th, 1973; Murray and Gi 11, 1978), and a large fraction of the particulate iron in rivers, salt marshes and sea water is in the forms of ferric oxyhydroxides and clays (c.f. Hem and

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138 Cropper, 1959; Stumm and Lee, 1960; Towe and Bradley, 1967; Eckert and Sholkovitz, 1976; Byrne and Kester, 1976,1978, 1981; Boyle and Edrrond, 1977; Davison, 1979; Luther, 1982; Mayer et al., 1982; Fox and 1983; Giblin and Howarth, 1983; Fox, 1984). A small fraction is incorporated into organisms (Goldberg, 1952; Lowenstam, 1962; Duinker, 1981; Cowen, 1983; Collier and Edrrond, 1984), and the rest is deposited on the sea floor primarily in the oxidized state (Clarke, 1924; El. Wakeel and Riley, 1961; Sutill et al., 1972; Bagin et al., 1975; calvert, 1976; Chester and Aston, 1976; Marshall, 1983). During early diagenesis (c.f. carroll, 1958; Berner, 1969,1980 ; Drever, 1971b; Ehrlich, 1972; Presley et al. 1972; Aoki et al., 1974; Rozanov et al., 1974; Lundgren and Dean, 1979; Rozanov et al., 1980; Balzer, 1982; Davison, 1982; Nealson, 1982; Sorenson, 1982; Lyle, 1983; Sawlan and Murray, 1983; Tirrofeyeva, 1983; Colley et al., 1984; Van Houten and Purucker, 1984), and perhaps especially during deep burial (c.f. Muffler and White, 1969; Hower and Mowatt, 1966; Hower et al., 1976; Dunoyer de Segonzac, 1970; Perry and Hower, 1970; Weaver and Beck, 1971; Eslinger et al. 1979; Velde, 1985; Ahn and Peacor, 1985), ferric iron in sediments is significantly reduced to ferrous iron. Following uplift the iron is again oxidized, and the cycle repeated. Much of this chapter then is concerned with the redox cycling of iron on a global scale, both at the present time and in the past. First the sizes and distribution of the rrodern major sedimentary iron reservoirs are presented. Today's weathering fluxes from the continents are then calculated based on several assumptions, and the oxidation of iron upon weathering is briefly considered A discussion of published analyses of ferric and ferrous iron in modern sediments is followed by a

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139 consideration of the question of when the majority of iron reduction takes place. Observed trends in the Fe11/Fe111 ratio with geologic time are presented. Finally, to quantitatively assess the long-term trend in the redox state of iron, two independent calculations of the mean F II/F III t d. t e e ra 10 m se 1men s are presented. These calculations sho w that there may have been significant transfers of iron between the reduced and oxidized reservoirs over Phanerozoic time Sedimentary Iron Reservoirs The reservoir estimates presented in Table 5 are based on analyses of hundreds of samples of Russian and North American sedimentary rocks by Ronov and his colleagues (Ronov and Yaroshevskiy, 1976; Ronov, 1982, and references cited therein). The volumes and masses of continental sediments are divided into those of geosynclinal and platform affinity, and then subdivided into the major types of sedimentary rocks: sands, clays, carbonates, evaporites and volcanics. The chemical composition of each of these classes of rocks is presented as the percent of the major oxides. The sediments of the continental shelf and slope are assumed to be equivalent in composition to the continental sediments. OCeanic sedimentary mass is subdivided into the mass of surface (pelagic) sediments of Seismic Layer I and those of the sediments of Seismic Layer II, although the composition of Seismic Layer II sediments is assumed to be identical to that of Layer I The pelagic sediments are further divided into terrigenous, calcareous, siliceous, red clay and volcanic components Ronov's total sedimentary mass, excluding volcanics, is 2lt,200 X 1020 g, of which approximately 5% is iron expressed as Fe2o3 The

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140 Tabl e 5. Moder n Iron Reservoir S i ze s Typ e Major Vol Mass Sed. Vol. Weigh t Fe III Fen sPY sgyp of Struct. 106 10 2 .. Type % % Crust Units km3 g Fe 203 FeO ( 10 18 moles) p sand 22. 5 2 17 1 72 33. 0 29. 1 11.4 5 2 L c l ay 4 6 ;3 2 .61 113 9 0 .8 18; 1 A 220 0 .54 ca rb 2 4.3 0.7 8 1 2 8 8 6 7.0 44. 1 T e va p 0;20 0 3 ....; -'-41.0 F vol e* 4.4 4 .36 7.47 12.9 2 4 7 0;2 0 Avg/Tot 2.54 1 7 1 ;8 1 53;3 47.2 113. 3 c R A vg/Tot 100.0 172. 9 153 2 108. 6 0 M w/o vole 95.6 1 159. 9 128. 5 50. 3 108.4 N T G sand 20. 3 2.39 2.65 82. 0 101 .0 13.8 3.2 I E c l ay 40.9 3.63 231 279. 0 39 1 1 4 8 N 0 540 1.35 carb 1 9 2 0.59 7.1 0.8 E s ev a p 0.17 0 .04 1 0.0 N y vole* 19. 4 3 .08 5 82 101 0 212. 2 3.0 0.3 T N A vg/Tot 100;0 3 .06 424. 4 5 7 5 .0 61.9 30. 5 A c Avg/Tot 1 00.0 2;57 3 .29 6 1 8 3 63.0 L L w/o vole 80.6 2;44 2 .68 60.0 27 ; 2 N (all clastic S as FeS2 w/o voles) 77.9 A Avg 100. 0 2 52 2.72 596.5 715.5 107. 9 137 9 v 760 1.89 Avg 1 00.0 2;56 2 .93 606. 8 771 .5 113.3 1 36;1 G w/o vol e 492. 8 1 28;2 117;6 SUB-SHELF Avg* 100. 0 2.52 2 .72 126. 2 151 4 22.8 29. 2 CONTAND 160 0.40 Avg 100. 0 2;56 163. 1 24.0 INENT SLOP E w/o vol e 2.45 2.39 122. 7 133.1 27 24. 9 L terrig 7 3 5.00 1.91 8.7 3 7 1.2 A ca lcar 41. 5 2.55 0 .46 25.2 5. 1 o o y silica 4;92 1.1 5 19;9 5.2 O;O E rd ely 3 1 6;98 0.85 5L8 7 0 0 0 0 R 120 0.19 vole 3 0 5 .82 4 2 5. 1 0 2 c (70) t Avg/Tot* 100.0 4.61 0.97 109. 7 2 5 .7 1.5 E I Avg/Tot 100 0 1 109. 8 26.0 1.5 A w/o vol e 97;0 4;58 0 82 105. 6 20. 9 1.3 N LAYER Avg* 1 00 0 0;97 173.2 40. 5 I 120 0.30 A vg 100.0 4 ;75 1 42;2 2 3 c II w/o vol e 97. 0 4 .58 0 .82 166. 9 33. 2 2 0 A Avg* 100. 0 4 .61 0 .97 282.9 66.2 3 8 v 240 0.49 Avg 100 0 4.75 1 .01 288.3 68. 2 3.8 G ( 196)t w/o vole 4.58 0 .82 272.5 1 3 2 TOTAL 1100 2.74 Avg* 100 0 2.87 2.40 984. 9 915. 3 132.5 164 5 SEDI-900 w/o v 81.8 2 .82 1 89 631; 3 122 8 MENT 1160 2 .78 Avg 1 00.0 2.94 2.59 1023.3 1002.8 141 165.0 MASS 101 4 2.4 2 w/o v 87.4 2 93 2 14 888. 0 158. 5 calculated from Ronov' s averages t volume compacted to 2.5 g/cm3

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141 arrounts of ferrous and ferric iron in sedirrents are similar and total 722 and 888 X 1018 rroles, respectively. A calculation of the total arrount of sedimentary sulfide sulfur, corrected for the likelihood of misidentification of sulfide as sulfate in weathered, geosynclinal sediment outcrops (Helser et al., 1984) indicates that of the total ferrous iron in sediments, approximately 70 X 1018 rroles are combined wi t.h sulfur in pyrite. The remainder, roughly 650 X 1018 rroles is distributed between sedimentary silicates (clay minerals), carbonates, and oxides (magnetite) Ferric iron is a component of sedimentary silicates and oxides (goethite, hematite, and magnetite). The distribution of ferrous and ferric iron arrong the various rock types is shown in Table 6 (data from Ronov, 1982). The pattern of abundances for both oxidation states of iron is remarkably similar, with about 70% of all sedimentary iron occurring in clays, 24% in sands, and the rest in carbonates. Essentially no iron occurs in evaporite deposits. The distribution of iron among various mineral types is more difficult to ascertain. In well-drained soils, river sediments and oceanic surface sediments, the vast majority of the iron is in the oxidized form, and a considerable portion of this is in the form of oxide and oxyhydroxide coatings on grains (Towe and Bradley, 1967). Soils are generally treated with an reducing agent during analysis to rerrove these coatings (Mehra and Jackson, 1960; Sun et al., 1967); this process removes 5-20% or more of the total iron (Roth et al. 1969). Set ".1er and Angina (1980) analyzed 10 samples of river suspended-matter from Kansas for Fe associated with Mn-oxides, organics, colloids, and carbonates (Group A), soluble Fe and other metal coatings

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142 Table 6. Sedimentary Continental Vol % Fen Fe III % of % of % of Rock Type (10 18 moles) Fen Fe III Fer T T sand 24.7 130.2 115.1 24.4 23.4 23.9 clay 369.8 69.2 70;1 69.6 24.4 34.6 32.0 6.5 6.5 evap LO 0;4

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143 (Group B), and structural Fe in mineral grains (Group C). Group A was found to contain from .1 to .5% of the total iron, Group B, from 25 to 60%, and Group C, from 40 to 70%. On the average, 45% of the total iron was in the form of Fe-oxide coatings. Chester and Aston (1976) reported a similar analysis of the Mersey and Weaver rivers in the United Kingdom which showed that of the iron in the suspended sediment was not in the mineral lattice, i.e. it was soluble in an acid-reducing agent and thus was in the form of ferric oxides. Stream sediments are transported through estuaries where additional ferric oxides are often precipitated with organic colloids as fresh water and sea water mix (e.g. Boyle and Edmond, 1977; Murray and Gill, 1978; Fox and Wofsy, 1983; Fox, 1984), and are then deposited in oceanic basins. Average Atlantic deep-sea surface sediments contain about 20% non-lattice-held iron (Chester and Aston, 1976), while metalliferous sediments may contain as much as 70% of the total iron in the form of amorphous and crystalline ferric oxides (e.g. Bagin et al., 1975). If upon burial the sediment contains even a fraction of a percent of organic carb on, anoxic conditions will be developed as a result of the oxidation of the organic rna t ter. Under these conditions, and in the presence of sulfides in marine settings or carbonate ions primarily in non-marine settings (e.g. castano and Garrels, 1950; Huber and Garrels, 1953; Garrels and Christ, 1965; Curtis, 1967; Curtis and Spears, 1968; Berner, 1971; Pearson, 1979; Spears and Amin, 1981), ferric oxides are unstable and will dissolve and reprecipitate as ferrous sulfides or carbonates. Thus ferric oxides and hydroxides are rare in ancient sedimentary rocks (Fischer, 1963; Berner, 1971); where they occur in unweathered rocks they indicate that very little organic matter was

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144 or-iginally bur-ied with the sediment Because rrost mar-ine sediments contain some or-ganic matter-, fer-r-ic oxide-r-ich sedimentar-y r-ocks near-ly always have a non-mar-ine or-igin (Ber-ner-, 1978) Thus, in assigning sedimentar-y ir-on to its var-ious miner-alogical r-eser-voir-s, it appear-s that near-ly all of the fer-r-ic ir-on is in the octahedr-al sites of sedimentar-y silicates (clays). Fer-r-ic-oxide in continental or-ganic-fr-ee sediments is a small fr-action of the total mass of sedimentar-y ir-on. Fer-r-ous ir-on is also pr-edominantly found in silicate miner-als, however-, a substantial amount is combined with sulfur in pyr-ite. If the 888 X 1018 moles of fer-r-ic and the (722 total 70 pyr-ite =) 652 X 1018 moles of fer-r-ous ir-on ar-e assigned to a hypothetical silicate r-eser-voir-, the Feii/Feiii r-atio is 0.73, near-ly that of the aver-age shale (0.68) accor-ding to Clar-ke (1924). Weather-ing Rates A r-ather-r-ough appr-oximation of the pr-esent-day continental weather-ing r-ates of fer-r'Ous and fer-r-ic ir-on can be made fr-om the data in Ronov (1982) and Milliman and Meade (1983) This appr-oach is based on a numberof assumptions. One is that the aver-age weight per-cent of the elemental oxides forspecific types of platfor-m and geosynclinal sediments is globally r-epr-esentative, so that differ-en ces in the per-cent FeO orFe2o3 arrong continents r-esult only fr-om differ-ences in the r-elative amounts of the differ-ent types of sediments, and theirassociation with eitherplatfor'ffi orgeosynclinal str-uctur-es. Anotheris that the total sediment flux (Milliman and Meade, 1983) comes fr-om the weather-ing of the var-ious types of sediments in the pr-opor-tion in which they ar-e found in unweather-ed sedimentar-y r-ocks. A thir-d assumption is

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145 that the volurre percentage of each sediment type is also its weight percent; the density of all sediments is assumed to be identical for lack of information on the distribution of densities. Data from Table 5 are used to calculate the average wt. % of the two iron oxides for the various rock types. Then, from the volume % of each rock type for each continent (Ronov, 1982), one can calculate the weighted average percent of FeO and Fe2o3 in the sediments of each continent, Which is assumed to be that of the suspended load of streams draining the continents. Multiplication of these percentages with the total sediment flux gives the particulate flux of ferrous and ferric oxide from each continent to the world ocean (Table 7). A couple of important points need to be emphasized at this stage. Firstly the flux of ferrous iron from the continents is only in terms of the unweathered rock. Several soil profiles from a variety of rock types and ranging in age from the modern to the Proterozoic are shown in Figure 38. In addition, Table 8 lists the percent of the ferrous iron oxidized during weathering for a variety of igneous and metamorphic rock types. The common feature despite a wide range in total iron contents and weathering conditions is the nearly complete oxidation of iron upon weathering. Thus as previously stated m ost of the iron in streams is in the ferric state, which raises the second point. The large part of the total flux of iron from the continents is present in the suspended load of streams. Ferric iron is extremely insoluble in river or seawater, and it precipitates as ferric oxyhydroxide colloids Which often contain organic matter as well. The ratio of the d i ssolved load of iron to its total load in rivers is thus very small ( 0. 2%, Martin and Meybeck, 1979).

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146 Table 7. Iron Weathering Fluxes Structure Sedim:mt Type Avg Wt% FeO Avg Wt% Fe2o3 platform sand and clay 2.32 3.15 (p) carbonate 0;47 0;78 evaporite 0.20 volcanic 4.36 geosynsand and clay 3.30 3.03 cline carbonate 0.59 (g) evaporite 0.04 0.17 volcanic 3.08 Continent Sedim Vol Weighted Weighted Sed Flux Type % % FeO % Fe2o3 Flux Fen Fern p/g p/g p/g avg avg 106t/yr 10 12l1Dles/yr Eurasia snd+cly 62.5/57.7 + Oceanic carb 1.84/3.13 2.37/2.46 9663 3.77 2.95 Islands evap 3.2/0.2 2.80 2.44 vole 3.2/17.7 North + snd+cly 64.8/51 .o Central carb 1.89/3.51 2.41/2.56 1462 0.64 0.46 America evap 4.1/0.3 3 .16 2.53 vole 3.5/28.4 South snd+cly 82.5/73.1 America carb 8.4/8. l 2.60/3.50 3.04/2.83 1788 0.82 0.64 evap 0.5/0.4 3.28 2.88 vole 8.6/16.5 Africa snd+cly 76.1/80.7 carb 2.30/3.11 2.80/2.72 530 0.19 0.18 evap 1.1/0.0 2.59 2.77 vole Australia snd+cly 76.2/72.1 carb 2.09/3.77 2.68/2.94 62 0.03 0.02 evap 3.22 2.86 vole Total 1 3,505 5.44 4.27

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Table 8 Iron Oxidation During Weathering Rock Type Location Fe II Fe II % of Feii Reference fresh altered oxidized (mmol/100 g rock) Igneous dolerite Br. Guia n a 155.9 20.8 87 Guiana 114. 9 16. 2 86 diabase Guinea 85:7 0.0 100 basalt Java 96. 0 0.0 100 Hawaii 129. 4 2 5 98 andesite Hawaii 95. 2 21.9 77 Hawaii 98.3 28. 1 71 Hawaii 96.0 27. 5 71 Hawaii 8L9 15. 8 81 Java 78 epidiorite Br. Guiana 62.8 0.0 100 qtz monzonite Madagascar 66.7 78 neph-syenite Madagascar 30;5 0 0 100 granite Br. Guiana 4;2 -33 Metamorphic hrnbl-schist Br. Guiana 137.5 16. 9 88 amJilibolite Caroline Is. 119.2 0 0 100 gran .-gneiss U. States 2;9 87 1 --Mohr and van Baren (1954) and references cited therein 2 --Patterson and Roberson (1961) 3 --Goldich (1938) 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 3 147

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Figure 38 A,B. Modern soil profiles of Fe11!Fe111 A. A shalederived till (Fanning and Jackson 1966). B; a laterite on dolerite (Mohr and van Baren, 1954).

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149 0 T I I I C\1 Ill -0 --. 0 0 --. C\1 I I I I I 0 0 C\1 '
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Figure 38 C,D. Paleosol profiles of Fe11!Fe111 C. Late Paleozoic paleosol on granodiorite (Wahlstrom, 1948). D. Mid-Proterozoic paleosol on meta-arkose (core 20, MacDonald, 1980, i n Holland, 1984).

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0 0 .... u 0 (T) 0 0 N (T) (W) MOI38 H.Ld30 (W) 3/\0BV 151 0 co 0 (T) 0 0 0 0 oCT> '
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152 According to the calculations performed for Table 7, 9. 7 x 1012 rroles of ferric iron are transported to the sea each year. This compares with the value of 12.9 X 1012 rroles/year in Martin and Meybeck (1979). Their larger value arises from two sources: a larger estimated percentage of Fe in the particulate load (4.8% vs. 4.0% here) and a larger estimated global sediment flux (15,000 X 106 t/yr vs. 13,505 X 106 t/yr here). Of the total flux of Fe weathered from the continents, approximately 56% comes from the weathering of reduced iron in silicates and pyrite and 44% comes from the weathering of oxidized iron minerals, mainly silicates. Ir:'On in Modern Sediments and Early Diagenesis The determination of ferrous and ferric iron in sediments has been either by laborious and imprecise wet chemical methods or by the rrore precise yet new and more expensive method of Mossbauer spectroscopy. In either case, because of the difficulties involved, rrost analyses of iron in sediments have been for total iron only. Thus the discussion which follows on the global distribution of ferrous and ferric iron is based on a limited data set; it is hoped that in the future the determination of the oxidation state of iron will become a routine task during sample analysis. El Wakeel and Riley ( 1961) published what is perhaps the rrost complete compilation of deep-sea sediment analyses of samples collected throughout the world. Figure 39 shows the global distribution of Feii/Feiii ratios is surface sediments. In general there is an increase in this ratio with increasing latitude and with proximity to the continents. The global distribution of reduced to oxidized iron matches

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Figure 39. Global distribution of chlorite (percent of <2ft1 frffFion contoured in 20% increments; Griffin et al. 1968) and Fe /Fe in modern, oceanic surface sediments (El Wakeel and Riley, 1961).

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Fe11/Fe111 <10 -<0.25 A 10 0 .25-0.50 B 0 0 .50-0.75 c 0 >0.75 0 0 # OF OCCURRENCES 10-20 20-30 30-50 6 1 0 5 1 0 0 2 0 2 3 0 oo 1.}1 .s::-

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155 quite well with the global per:'centage distribution of chlor:'i te in the clay size fr:'action of deep-sea sediments (also shown in Figure 39; Gr:'iffin et al., 1968). The number of occurr:'ences of oxidized samples is significantly higher in the sediments which ar:'e low in chlor:'ite, whereas the highly r:'educed samples only occur:' in the high chlor:'i te peroentage zones (Figur:'e 39 inser:'t). This suggests that at least par:'t of the t:' II/F III d t th f . mcr:'ease m re e 1s ue o e pr:'esence o chlor:'l te, which 1s basically a fer:'r:'ous miner:'al (Feii/Feiii==7; Foster:', 1962). However:', El Wakeel and Riley (1961) remar:'k on the COr:'r:'espondence among high Feii/Feiii mtios and the per:'centage of Or:'ganic car:'bon and r:'educed natur:'e (green color) of the sediment, which would indicate a diagenetic r:'ather than depositional Or:'igin for the ferr:'Ous iron in some sediments. El Wakeel and Riley's (1961) oceanic aver:'age weight peroents of Fe2o3 (4.89%) and FeO (0.94%) give a mean Feii/Feiii ratio of 0.21 for:' sur:'face sediments. The abundance of ferr:'ous ir:'on is primar:'ily the r:'esult of two pr:'ocesses: the sedimentation of detr:'i tal, reduced iron miner:'als and the early diagenetic r:'eduction of fer:'r:'ic oxides and silicates (volcanic sediment sour:'ces of ir:'on play a minor:' role in the sediment budget of the wor:'ld ocean; Chester:' and Aston, 1976). The cor:'r:'espondence of the distr:'ibutions of the abundance of chlor:'i te in clays and the green reducing make it difficult to discr:'iminate between the two pr:'ocesses. The color:' of mar:'ine sediments does indeed seem to be closely tied to the oxidation state of ir:'on, especially to that in clay miner:'als. Clays in the oxic zone of marine sediments ar:'e character:'istically r:'ed, br:'own, or:' tan, while clays in anoxic sediments ar:'e gr:'een. Lyle ( 1983) has derocmstrated that the br:'own to gr:'een color tr:'ansi tion in hemipelagic

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156 sediments is a result of the reduction of iron in smectites, and occurs at the depth in the sediment where appreciable arrounts of aqueous ferrous iron are found A pelagic sediment/turbidite sequence from the northeast Atlantic (Colley et al., 1984) also shows an increase in the ferrous/ferric ratio in turbiditic green clays sandwiched between brown pelagic deposits. The green muds are not nearly as reduced as those studied by El Wakeel and Riley (1961) however, with a Fe11!Fe111 ratio of .. 0.15; the brown clays have an average ratio of 0.02. Apparently much of the reduced iron was mobilized and precipitated elsewhere in the sediment as ferric oxides (vecy little sulfate reduction was occurring in these sediments) The ubiquity of a brown to green vertical color change in oceanic, terrigenous or hemipelagic mud cores indicates that a measurable amount of iron reduction occurs during the early diagenesis of clay minerals. This quantity however may be quite small. In the experimental reduction of iron in nontronite (an iron-rich smectite) by hydr azine, nontronite underwent an instantaneous color change from yellowish to green, despite the fact that only a small proportion of the ferric iron, <8%, was reduced (Rozenson and Heller-Kallai, 1976a) Other, stronger treatments are capable of removing structural iron from clays (Rozenson and Heller-Kallai, 1976b, 1978; Stucki and Roth, 1977; Stucki et al. 1984a,b) This is consistent with the findings of Colley et al. (1984) menti oned above. The formation of pyrite in anoxic se diments requires the reduction and mobilization of ferric iron. The more easily reducible ferric iron coatings on clay particles provide much of the iron for pyrite formation, however, silicates are known to lose iron in the presence of

PAGE 173

157 sulfides (Rozenson and 1976b). In either:case the pyr-itic ir-on in shales is a small of the total (<10% of FeT, Table 5), so that the amount of to form te is small. The global distr-ibution of redox states in sediments could be explained by diagenetic but points ar-gue against this 1) the of in clays is upon to oxygenated water-air-; 2) El Wakeel and Riley ( 1961) took no precautions to that this did not occUr:'; 3) the aver-age state of oceanic sediments, Feii/Feiii of 0.21, could easily be explained by the 12% of oceanic clays which (value Gr-iffin et al., 1968). This would have to have an of Feii/Fe111 of 1 .75 to give the oceanic mean if all sediments completely oxidized. This value is well within the 1962). the obser:-vations and of E1. Wakeel and Riley ( 1961 ) suggest that in fact the state of in oceanic sediments is determined post-deposi tionally. They obser:-ve that the content of fer-r-ous in the sediment is low but is in sediments with amounts of Indeed, as 40 shows, is a good between the and the amount of preser-ved in samples. If the of in sediments is diagenetic II III then the between Fe /Fe and % may be

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Figure 40. Relationship between Fe111Feiii and weight percent organic C in modern, oceanic surface sediments (El Wakeel and Riley, 1961).

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159 T T I 1 I E) E) 0 u lJ E) n:: E) E) 0 E) E) E) E) EE) E) E) E) t-E) E) E) E) 3 E) e lJ E) E) 0 E) -__J -I E) E) I I I I I N I I

PAGE 176

coincidental. 160 The unlikely relationship between organic carbon and chlorite percentages is then marely a result of the less-than-global sample coverage and the tendency towards high organic productivity and low chemical weathering rates at high latitudes. Sampling of surface sediments where chlorite is high and organic carbon percentage low, perhaps in the areas west of Australia or near the northeast coast of canada would help to resolve this issue. Deep Burial, Metamorphism, and Iron Reduction The evidence presented thus far argues that very little iron reduction takes place during early diagenesis. The srrall quantity of iron that does get reduced at that stage comes primarily from relatively labile ferric coatings on grains, and largely goes towards the production of pyrite in the sulfate reduction zone of shallow, terrigenous sediments (Berner, 1984). A considerable amount of reduction then must occur durin g deeper burial so that the average ferrous/ferric ratio in shales o f 0 .68 (Clarke, 1924), in low-grade pelites of 1.06 (Shaw, 1956), in slates of 1.81 (Eckel, 1904) and in high-grade peli tes of 2 62 (Shaw, 1 9 56) is achieved (these references taken from Garrels and Mackenzie 1971a). Direct evidence of the reduction of iron during later diagenesis and metamorphism comes from a limite d number of cores and outcrops representing sequences of sediment alteration with little overprint from variations in the initial sediment c omposition. These include cores of the mixed-layer clays of the Gulf Coast Tertiary (Burst, 1969; Perry and Hower, 1970; Weaver and Beck, 1971; Hower et al., 1976; Boles and Franks, 1979; Velde, 1985; Ahn and Peacor, 1985), cores of Pliocene and

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161 Quatet"nat"y Colot"ado Rivet" delta sediments from California (Muffler and White, 1969; Thompson and Jennings, 1985), cores of the Cretaceous mixed-layer' clays of Africa ( Dunoyer de Segonzac, 1969, 1970), cores from Cretaceous and Tertiary sand and shale sequences in the Rock y Mountains (Pollastro, 1985) and samples from outct"op of a variety of bentonites ( Hoffman and Hower, 1979; Eslinger et al., 1979; Howard and Roy, 1985) and illites and smectites (Hower and Mowatt, 1966 ) From this list of studies only a few contain analyses of ferric and ferrous iron (Hower and Mowatt, 1966; Muffler and White, 1969; Weaver and Beck, 1971; Eslinger et al., 1979). The primary concern of the majority of these studies has been the conversion of mixed-layer illite/smectites to ordet"ed illites with a low proportion of smectite layers (Garrels, 1984). This change is believed to be brought about by the substitution of Al for Si i n t h e tetrahedral layer of the clay, leading to an increased positive charge deficit that is preferentially satisfied by the easily-dehydrated K+ ion (Eberl, 1980). The supply of potassium is from the dissolution of potassium feldspar or detrital mica, either of which may show a significant de crease with depth in the sediment, and may often limit the extent of the conversion (Srodon and Eberl, 1984; Thompson and Jennings, 1985). other general depth trends across the zone of conversion (50C to 200C) are the dehydration and decrease in expandability of the clay, a decrease in the abundance of calcite and kaolinite, t h e appearance and gt"owth in both size and abundance of chlot"i te, a loss of silicon and iron and an increase in Al in the < 1 }.B1l fraction of t h e clay, and the reduction of iron. The contribution of the reduction of iron to the increase in

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162 structural charge of the clay has been assessed by Eslinger et al. ( 1979). They proposed that 10-30% of the structural charge increase could be due to iron reduction, although there was too much scatter in their data to be conclusive. Figure 41 plots the relationship between Fe II /Fe III and weight percent K 2o for these K -bentonites and for a variety of mixed-layer clay series and samples. The general trend is one of increasing %K2 0 with increasing Fe II /Fe III but the various sequences or group of samples exhibit peculiar characteristics. The samples of Hower and r-bwatt (1966) display an iron reduction-independent increase in %K2o until very high percentages are reached, at which point Fe begins to be reduced as K continues to be fixed into the clay lattice (%K2o increases). An essentially similar pattern is shown by the bentonites of Eslinger et al. (1979). The Salton Sea Hydrothermal Field samples show a much steeper increase in Fe II /Fe III with K 2o and acquire much higher iron redox ratios than the other samples. The Salton Sea trend is also closer to that of the average Phanerozoic shale-slate trend. It is produced not only by the illitization of smectite but by the subsequent conversion of illite to mica and progression into the low-grade metarrorphic greenschist facies of quartz + epidote + chlorite + K-feldspar + albite +1K-mica (Muffler and White, 1969). A comparison with the data of Nanz ( 1953) on the chemical composition of Precambrian lutites (i.e. pelites, shales, slates) suggests that at low Feii/Feiii ratios (and low grade of metarrorphism; see below) a wide range of weight percent K 2o values are observed (Figure 42), whereas at higher ratios and higher grades they converge on a value of roughly 3-4 wt. % K 2o ( a value, not plot ted, with a

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Figure 41. Relationship between weight percent K20 and Fe11!Fe111 for a variety of mixed-layer clays. ( +) various illites and illi te/smecti tes from Hower and Mowatt, 1966; (X) bentonites from the disturbed belt of Montana from Eslinger et al., 1979; (6) borehole samples of the I.I.D. Geothermal Well #1; and (e) from the Wilson #1 Well from the Salton Sea Hydrothermal Field (Muffler and White 1969); (SH) the mean shale (Clarke, 1924); (SL) the mean slate (Eckel, 1904); (LP) and (HP) the average lowand highgrade pelite o f Shaw (1956).

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164 0 ..; 0 (T) ... .... .... QJ lL ........ .... .... QJ a lL .. N + f1 E) a + ..... i + + + + + X E) a 0 aci . . a CD (0 N 0 .....

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Figure 42. Relationship between weight percent K20 and Feii/Feiii in the Precambrian lutites (i.e. shales, slates, pelites) of Nanz (1953).

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166 0 a ..-4 E) E) 0 (I) E) E) E) E) 0 E) i ..... ..... ..... E) Ql E) IJ_ E) ..... E) .... Ql E) 0 IJ_ E) 0 E) E) N E) E) E) E) E) 0 0 0 0 0 0 od . I 0 (I) CD (\J a -

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167 II III Fe /Fe of ==60 was 3.5 wt. % K20). The idea then is that upon matarrorphism the diverse suite of minerals represented by the sedimentary package are recrystallized into a more uniform group of minerals in the greenschist facies. It is then fairly well established that Fe11/Fe111 increases during burial. However, what has been presented thus far does not provide any direct information on the cause or timing of the reduction of iron in clay sediments (cf. Addison and Sharp, 1963; Desprairies, 1983; Lear and Stucki, 1985). A common belief is that this reduction process occurs over a very limited temperature range, yet this has not been demonstrated by chemical determinations or laboratory studies (Velde, 1985). The borehole data of Muffler and White (1969) and Weaver and Beck (1971) contain the information needed to test this assumption. Figure 43A shows the Fell /Fe III ratio of the bulk samples as a function of depth in these holes. Note both the general increase in this value with depth and the difference in slope among the three sets of data. This difference can be related directly to the geothermal gradients of each location (Figure 43B). The I.I.D. Geothermal #1 well displays pronounced geothermal and Fe11/Fe111 gradients compared to the Chevron borehole, which has shallow gradients of both. The Wilson #1 well is intermediate to the other two. As one would expect, a plot of Fe II /Fe III vs. temperature gives a clear indication of the effect of increasing temperature on the reduction of iron (Figure 44). The relationship appears linear. The scatter above 300C is probably related to the abundance of chlorite (the dominant ferrous mineral) relative to either or both of the following: the abundance of pyrite which is unfortunately reported as ferric iron (this also accounts for

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Figure 43. Data from various boreholes on A) Feii/Feiii and B) the geothermal gradient. Symbols same as in Figure 41, except (X) are from the Chevron borehole (Weaver and Beck, 1971).

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169 0 0 ...... m ...... ... 0 ... 0 ... (T) A ... u 0 0 e 0 v N ... e ... e 1-0 e tl4 0 e tl4 .... e w 0 00 0 0 .... II) 0 II) < 0 ...... ..... 0 ..... ..... Ql (I') ... 0 ll... N .... .... f) ... ... e 0 Ql w M M w ll... e .-4 E) 0 0 0 00 0 .... II) (W) Hld30

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Figure 44. Relationship between Fe111Fe111 and temperature at depth in the crust; data are those of Figure 43.

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I I l I I I I I I --- E) E) -I I I I l I l 0 0 0 0 . . If) (T) N E) E) I I 0 ..... E) 0 0 (T) -0 0 N 0 0 ..... 00 0 171 r-. u 0 v r-

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172 much of the scatter in Figure 43A), and the abundance of epidote which is indeed a ferric mineral. The most likely reductant for iron in these environments is organic carbon (kerogen) The oxidation of kerogen by iron can lead to the production of a variety of dissolved organic species (Table 9; Surdam and Crossey, 1985) which themselves can be further oxidized by iron (Kharaka et al., 1985). It is suggested then that the thermal degradation of organic matter, and perhaps the oxidative degradation of the kerogen by iron, liberates organic acids which with dissolved iron control the redox state of both the porewaters and the clay minerals as well. The quantitative effect of iron reduction on the amount of organic carbon in sediments has been assessed by Surd ham and Crossey ( 19 85) They used the stoichiometry of the reactions in Table 9 and several reasonable assumptions to predict the percent of the original kerogen which would remain after the reduction of a typical amount of iron in a shale. The results of their calculations for the conversion of kerogen to acetate, co2 or other more complex molecules clearly shows that the reduction of iron can have a major effect on the preservation of organic carbon especially in sediments which contain small amounts of kerogen. The Global Iron Cycle Figure 45 is a schematic representation of the global iron cycle based on the foregoing discussion. The description of a cycle can begin anywhere in the cycle; here it will begin with the depositio n of predominantly oxidized riverine sediments in the ocean These sediments contain ferric iron which resides primarily in clay minerals (smectites,

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KeroPro Gen Duct Type I Acetate II Acetate III Acetate I Oxalate II Oxalate III Oxalate I Hydro-II quin-III one 173 TABLE 9. Iron-Kerogen Reactions Reaction CH1 72o0 12+ Fe2o3 + H 2 0 0.5 CH3COOH + 1.48 FeO CH1 28o0 18+ 0.46 Fe2o3 + 0.36 H 2 0 0.5 CH3COOH + 0.92 FeO CH0 88o0 20+ Fe2o3 + H 2 0 0 5 CH3COOH + 0.48 FeO CH1 .72o0 .12+ 2.24 Fe2o3 0.5 H 2c2o4 + 0.36 H 2 0 + 4.48 FeO CH1 .28o0 18+ 1.96 Fe2o3 0.5 H 2c2o4 + 0.14 H 2 0 + 3 92 FeO CH0 88o0 20+ Fe2o3 + 0 .06 H 2 0 0.5 H 2c204 + 3.48 FeO CH1 72o0 12+ Fe2o3 0.17 H 2c6o2 + H 2 0 + 1 .82 FeO CH1 28o0 18+ Fe2o3 0.17 H 2c6o2 + H 2 0 + 1 .26 FeO CH0.8800.20+ 0.41 Fe2o3 0.17 H 2c6o2 + 0 .28 H 2 0 + 0.82 FeO From Surdham and Crossey, 1985

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Figure 45. Schematic of the global Fe redox cycle showing the relationships between weathering and oxidation, burial and reduction.

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Fe111-CLAYS + Fe111-0XIDES MOLES/1 06 yr -s?????00?????:::::::-00900900?9s I A. Fe11/Fe111=0.8 I I (Fe111>>Fe11 )-CLAYS BURIAL INCREAS\tlG \ \ \ _. Ul

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176 illites, and and in coatings on If these sediments contain even a small arTXJunt of the oxide coatings will be and if a supply of sulfide exists (via sulfate the will precipitate as sulfide minerals. The reduction of a small amount of iron in the clays may also at this time, in the zone of diagenesis. With increasing burial temperatures and more is reduced as chlorite grows at the expense of smectite, illite, and kaolinite. The reductant once again is organic carbon (kerogen). Depending on the tectonic setting the sediment package may may not be uplifted and once again exposed to surface conditions before a large amount of iron reduction takes place. During the structural iron is completely oxidized with some of it in the silicate and some of it being released and precipitated as ferdc oxides and These weathering products are and by streams to the ocean, completing the cycle. Temporal in the Ratio of Rocks The of changes in the chemical composition of sedimentary rocks time continues to be an interesting and endeavor (see Garrels and Mackenzie, 1971 a; Ronov, 1982; Holland, 1984). Accordingly, the increase in the oxidation state of in fine-grained time is subject to Figure 46 shows Feii/Fe1II in a of shales and slates of ages dating from the

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Figure 46. Temporal trends in Fe111Fe111 through geologic time. North American and Russian platform data from Ronov ( 1982); Williston Basin data from Aliani (1983)

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I I I 1-- < 1-(T) ..J < (I) a.. ..J m a.. v 0:: z w < X -z < (J) < (J) :J ..J z 0:: < I I e f-!-E) f-f-e I I I 0 0 a) u) I I e I e E) e I I I 0 0 N I I E)] 0 e rl E) -----0 0 0 0 0 0 N 0 0 0 (1') 0 0 co 0 w c.:> < 17 8

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179 to the Present. The data of Ronov (1982) are EOn or Period averages while those of Aliani ( 1983) are for particular occurrences. The general trend indeed is a decrease in the Fen /Fern ratio over the history of the earth. One possible explanation for the increase in the oxidation state of sedimentary iron through time is a gradual increase in the "intensity" of surficial oxidizing processes via the accumulation of oxygen in the atrrosphere. This is the interpretation favored by Ronov ( 1982) and Aliani ( 1983) It implies non-reversibility in the oxidation of iron such that the ferric reservoir grows at the expense of the ferrous reservoir through time, i.e. the reduction of iron during burial of ferric minerals does not restore the original redox ratio of the previously unweathered parent rock. An alternative interpretation of the trend is that it is not primary, but rather reflects the gradual reduction of ferric iron by kerogen via metamorphism (Garrels and Mackenzie, 1971a). Simply stated, the likelihood of a sediment becoming meta.rrorphosed increases as a sedimentary unit ages. Other chemical and mineralogical trends which parallel the diagenetic sequence for shales discussed above tend to support this interpretation. The second alternative is a uniformitarian interpretation because it implies that in the past, as is the case today, the iron minerals were largely oxidized upon weathering. Indeed, Precambrian paleosols often display the extensive oxidation of iron characteristic of rrodern, well drained, oxygenated soils (Figure 38). However, the deposition of the Precambrian iron formations seems to have required the transportation of iron in the ferrous state; earth surface conditions, especially P02

PAGE 196

180 must have been considerably different at these early tirres. Nevertheless, even at low P02 the oxidation of iron during weathering could have been extensive (Holland, 1984). Much of the preceding discussion in this paper, especially that which considered the timing of Fe reduction, supports the interpretation that the increase in the Fen /Fern back through tirre is primarily the result of increase in the rreta.rrorphic grade of a rock as it ages. Accentuating this change perhaps is the possibility of initially higher Fe11/Fe111 ratios of Archean and Proterozoic weathering products. This conclusion however rests upon unstable ground, and may well be shown to be incorrect as more data are accumulated. Phanerozoic Trends The available iron analyses of Ronov ( 1982) are Period averages at best, and detailed Phanerozoic trends in the Fe11/Fe111 ratio cannot be resolved from them (Figure 46). The Russian Platform data show no trend whatsoever for the Phanerozoic whereas the North American Platform data show a continuous decrease in this ratio from the late Proterozoic to the present. Analyses of shales from the Williston Basin (Aliani, 1983) present quite a different picture of the Phanerozoic (Figure 46), with generally low Fe11!Fe111 ratios punctuated by periods (the late Carboniferous and Tertiary) of higher ratios. The weight percent Fe2o3 is fairly constant for these samples; the variation occurs in the FeO composition. It is impossible at this tirre to assess whether this Phanerozoic pattern is representative on a global scale or is only of regional applicability. Comparisons will now be made to calculations of the Phanerozoic

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181 Feii/Feiii trend based on the relative proportions of platform and geosynclinal depositional environments through time, and to others based on a model of the global Fe-e-s cycle. Calculations of the Phanerozoic Trend in Fe11!Fe 111 Two approaches are used here to make crude calculations of the relative proportions of Fe II and Fe III in sediments deposited at any given time in the Phanerozoic. The first utilizes the data of Ronov (1982) on the iron contents of platform and geosynclinal sedimentary rocks and the variation in the amount of sediment deposited in each of these environments through the Phanerozoic. For these calculations it is assumed that the iron composition of the sediments in each environment is constant; variations in Fe II /Fe III arise due to the variation in the amounts of sediment deposited in platform (low Fe11!Fe 111 ) and geosynclinal (high Fe111Fe111) environments. This rather circuitous way of acquiring ancient ferric/ferrous ratios is necessitated by the fact that Ronov (1982) has not published his chemical analyses for all ages, but rather for the Period averages only. The second approach is based on a global sedimentary reservoir transfer reaction, modified from Garrels and Perry ( 1974), the stoichiometry of which is used to calculate burial fluxes of reduced and oxidized carbon, sulfur, and iron. The two approaches produce similar Phanerozoic trends which are not unlike those described above. The first set of calculations is the simplest. The Fe11/Fe111 ratio for platform and geosynclinal sediments can be obtained from Table 5. Using the overall averages from this table, these ratios are 0.89 and 1 .43, respectively. From Ronov (1982) the total volumes of platform and

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182 geosynclinal sediments for each time interval are then multiplied by their respective iron ratios, added together, and divided by the total volume of sediment deposited. The results are presented in Figure 47. There is a gradual increase in the Fe11!Fe 111 ratio through the early Paleozoic, a peak in the late carboniferous, a general decline in the ratio through the rest of the Paleozoic and Mesozoic, and a rise through the Tertiary. Note the significant perturbation in this trend at or near the Permo-Triassic and Cretaceous-Tertiary boundaries. (This method of calculation with extensions for the calculation of the original mass of sediments and their weathering rates, is essentially the inventory approach of Holser et al. (1984) In fact, if the rate constants for the ferrous and ferric reservoirs are assumed to be identical, the ratio of depositional rates calculated is identical to the Fei1/Feiii ratio presented in Figure 47.) The second method requires more explanation. It is based on a global transfer reaction that specifies the proportionality that must exist between the growth and diminution of the various sedimentary reservoirs if oceanic and atmospheric compositions are to remain constant (see the discussion in Chapter 1 and in Garrels and Perry, 1974). The transfer reaction used here is modified from Garrels and Perry (1974) to include the ferrousand ferric-silicate reservoirs, and to allow the growth of the dolomite reservoir at the expense of the calcite reservoir. Unlike the earlier version, the stoichiometry of this reaction i s not well constrained because of the inclusion of the third redox pair (Fe) 'IWo stoichiometries will be used to test the sensitivity of the calculations to the partition of the available reducing capacity of CH2o between the S and Fe pairs. If it is assumed,

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Figure 47. calculated Phanerozoic trends in Fe II /Fe III using two methods, one based on the surviving sedimentary mass and its relative abundances of platform and geosynclinal sediments (bars) and the other based a modified constant ocean-atmosphere model with two transfer reaction stoichiometries (see text).

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MODEL BURIAL-FLUX RATIO N 0 0 0 0 I() . ..... ..... ...... I ..... . ..... 0 0 0 of5 -184

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185 for example, that the "electron flux" is evenly split between the two the reaction becomes: 30 FeSio 3 + 2 FeS2 + 11 GaMg(Co3 ) 2 + 15 H 2 o = 15 CH2 o + 4 Caso4 + 16 Fe2Si05 + 11 MgSio3 + 7 Caco 3 + 3 Si02 An implication of this reaction is that the pyrite-iron flux is 1/15 of the silicate-iron flux. An alternative stoichiometry in which the pyrite/silicate iron flux ratio is 1/5 and the electron flux ratio 3/1 is: 15 FeSi0 3 + 3 FeS2 + 9 CaMg(co3 ) 2 + 3 Sio2 + 15 H 2 0 = 15 CH2 o + 6 Caso 4 + 9 Fe2Sio5 + 9 MgSio3 + 3 caco 3 This reaction is interesting for in reverse it approximates the observed diagenetic and metamorphic transformation in which CH2 o is used to reduce iron and sulfur and in which calcite and the Mg from clays is used to form dolomite. The model is in essence that described by Garrels and Lerman (1981, 1984) and in Chapter 1. It utilizes the carbon isotope record of Lindh (1983) in the calculation of the burial rate of organic carbon; other burial fluxes are determined by the stoichiometry of the transfer reaction. Weathering fluxes are assumed to be proportional to the size of the reservoir. The time-interval average ratio of the burial fluxes of ferrous iron (in FeSio3 and FeS2 ) to ferric iron (in Fe2Si05 ) is plotted in Figure 47, where the time intervals are the same as those used in the previous calculation. Note the following general characteristics of Figure 47: 1) the general decrease in Fe111Feiii over the Phanerozoic seen in earlier figures; 2) the pronounced peak at the Permo-Triassic boundary as seen

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186 earlier, and similar features for the Devonian and Jurassic/Cretaceous, which do not show on the earlier plots; 3) the general Tertiary increase in Fe11;Fe111 ; 4) the increased sensitivity when more of the electron flux (redox capacity) is apportioned to the iron-silicate cycle (the first reaction). Sunmary Observations and calculations of the redox state of iron in sedimentary rocks support the conclusion that, in general, sedimentary iron was becoming increasingly oxidized through much of the Phanerozoic, and that this trend was perturbed at times, for example, at the Permo-Triassic boundary. The paucity of data from the Proterozoic makes it difficult to determine whether this trend was an extension of a long-term Precambrian tendency towards increased oxidation of iron, or whether it was part of a cycle of increasing and decreasing redox states, perhaps driven by tectonic change. The latter interpretation is supported by the two sets of calculations presented above which are based on either tectonic changes (locus of sediment deposition) which may be cyclic (e.g. Fischer, 1984) or on the carbon isotope age curve, which oscillates without apparent trend through the late Proterozoic and Phanerozoic.

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187 CHAPTER 4. FURTHER EXTENSIONS AND IMPROVEMENTS OF THE MODEL The refinement of a rr.odel of a system as complex as the global geochemical cycle is an ongoing process which will continue for years to come. This process will involve both the addition of new subcycles and the modification of existing ones as new information becomes available and as our knowledge of the multitude of interactions grows. Numerous assumptions have been made in constructing the current model and these need to be tested with field, laboratory and computer techniques. Closer attention will also need to be paid to the interaction of processes which act at various time scales; in a nonlinear system such as this there is always the possibility of significant, lasting effects of short-term cycles on the longer term cycles and vice-versa (e.g. La saga 1980 ) Two extensions will be discussed in this chapter. First the iron cycle as described in Chapter 3 will be incorporated into the modified SLAG model of Chapter 2. Then a first step will be taken towards a more realistic model of the sedimentary cycle, one which considers each sedimentary reservoir as composed of several packets of sediment of various ages, each of which has a specific probability of being eroded and recycled at any given time. This will be shown to be an important step towards our understanding of the history of atrr.ospheric 02 The Incorporation of the Iron Cycle

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188 The existing global geochemical cycling models, including those discussed here, have considered only the carbon and sulfur subcycles in the calculation of the 02 budget. The exclusion of the iron subcycle has occurred for many reasons, including: 1) the iron cycle is poorly understood; 2) the reduction and oxidation of iron requires only a single electron transfer while carbon requires 4 (C02+CH20) and sulfur requires 8 the fluxes of iron would have to be correspondingly large to be significant in the 02 budget; 3) there is neither any record of change in the iron isotopic composition of sediments to use to calculate fluxes, nor is there much interest or even acceptance of the possibility of the fractionation of iron isotopes during sediment cycling. Chapter 3 was intended to improve our general understanding of the cycling of iron. calculations in that chapter showed that the iron fluxes could be quite substantial; clearly they should be included in the global redox model. The possibility of iron isotopic fractionation in sedimentary processes is quite intriguing. Stable Iron Isotopes Although it is a heavy element iron ranges widely in its stable isotopic masses, from 54 to 58. The isotopic composition is 5.8% 91.72% 56Fe, 2.2% 57Fe and 0.28% 58Fe (Valley and Anderson, 1947; Chenouard, 1965; Holden et al., 1984). Based on mass ratios alone it is conceivable that iron would be fractionated during low-termper.ature geochemical processes. Considering the microbiological involvement in

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189 the reduction and oxidation of ir-on (e.g. Rickar-d, 1969; Kleinman and Cr-er-ar-, 1979; Lundgr-en and Dean, 1979; Nealson, 1982) it apper:-ar-s quite r-easonable to suggest that ther-e may be significant var-iability in the natur-al abundances of the ir-on isotopes. Ear-ly wor-k (in fact the only wor-k) on the natur-al distr-ibution of ir-on isotopes found no significant var-iation among meteor-ites and high temper-atur-e igneous and metamor-phic r-ocks, within the pr-ecision of the measur-ement (Valley and Ander-son, 1947). Rankama ( 1954) sumnar'ized this wor-k and pointed out the appar-ent separ-ation in the r-atio 5 "Fe/5 7Fe among samples of native ir-on (2.60), pyr-ite (2.70), and sider-ite (2.77). He states: These differ-ences, if r-eal, might well be connected with differ-ences in the geological sur-r-oundings and pr-ocesses fr-om which the samples r-esulted. Consequently, the isotopic constitution of ir-on should be deter-mined, by moder-n methods, in carefully selected geological materials. The possibility of a biological fr-actionation of ir-on isotopes should also be investigated. No one appar-ently has taken up the gauntlet. Var-ious new methods forthe determination of stable ir-on isotopes have been developed pr-imar-ily by nutr-itional chemists who use ir-on as a non-destructive tr-acer-. These methods include chemical and electr-on impact ionization mass sectr-oscopy (Hachey et al., 1980; Johnson, 1982), and neutr-on activation (Schmidt and Riley, 1979a,b; Litman, 1979; Janghor-bani et al., 1980). The authorhopes to pur-sue this line of resear-ch in the near-futur-e. Kinetic Equations forthe Model of the Ir-on Cycle In the absence of a stable isotopic r-ecor-d forir-on one must r-esor-t to the constr-uction of flux relations based solely on our limited

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190 understanding of the operation of the cycle. The iron cycle presents a special problem in that much of the reduction of iron occurs long after deposition. The current, single-box reservoir rrodel is incapable of adequately dealing with post-diagenetic change; a several-box model, in which the post-depositional part of the cycle is compartmentalized, is clearly needed. In lieu of this modification, simplifications are made so that the iron cycle can be included in the global model. The weathering fluxes are relatively straightforward to specify. The oxidized iron-silicate reservoir is assumed to weather only in proportion to its size. From the estimated rrodern-day flux of 4.3 X 1018 moles/10 6 yr and reservoir size of 900 X 10 18 moles a rate constant of 0.00478 (106 yr)-1 is calculated. The reduced iron-silicate reservoir (650 X 1018 moles) weathers as do the other reduced components of the rrodel in proportion to both its size and the mass of atmospheric 02 With a flux of 5.4 X 1018 rnoles/10 6 yr the rate constant is 0.000219 (106 yr1o18 rnoles)1 These rate constants are subject to the same correction factors as the other rate constants of Table 4. The depositional flux relations are rrore difficult. In nature, after burial, ferrous silicates and calcite form at the expense of ferric silicates and organic carbon (e.g. Surdam and Cressey, 1985): 2 Fe2Si05 + CH20 + CaSi03 + Si02 4 FeSi03 + CaC03 + H20 (47) where the supply of calcium is either in aqueous ca 2+ or in the exchange sites of clay minerals (here simply written CaSi03). The extent of this transformation appears to be related to the temperature of burial (Chapter 3) If one assumes that in general an increase in global tectonic activity, as indicated by the mean global seafloor spreading rate, corresponds to increased subduction, it is possible to form a flux

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191 relationship for the reduction of iron that is of the form: (48) where F0f Feii is the present-day iron burial-reduction rate, F F is w, e the present day total iron silicate weathering flux and F F is this w, e value at any time during the run, and f is the spreading rate sr correction factor. The choice of F0f,Feii is arbitrary at this time; it is chosen to be equivalent to the weathering flux of ferrous silicate. The total weathering flux ratio is included to make the reduction rate a function of the supply of iron-clays to sediments. The net burial rate of ferric silicate (F f ,Feiii) is then just the difference between the total weathering rate of iron silicates and F f, Fe II, assuming for now that the authigenic formation and dissolution of iron silicates are negligible or in balance. The obvious problem with the timing of iron reduction, as mentioned before, cannot be adequately dealt with in the current model. As such it will be assumed that the reduction of iron liberates 02 and the oxidation of iron consurres 02 In reality, as equation 47 shows, the reduction of iron is accompanied by the oxidation of organic carbon. This reduces the amount of oxidizable carbon available when the sediment is re-exposed; this loss is co mpensated for by the increase in oxidizable iron. Thus there may be little net effect on the coupled cycle; iron is rrerely proxying for carbon. However, the lag time between the oxidation of iron during weathering and its reduction during burial may present a transient drain on atmospheric 02 that can only be assessed after the model has been improved. The incorporation of the iron cycle into the total model requires the addition to and modification of the kinetic equations of Table 4.

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192 Equation h now becomes: M'(02) = M'(orgC) + M'(py)/8 + M'(Fe!I-sil)/4 (h') and the following equations are added: M'(Feii_sil) = Ff F II-k F IIM(Feii_sil)M(02 ) (w) e wo, e M'(Feiii_sil) Ff,Feiii-kw,FeiiiM(Feiii-sil) (x) -M' (Fe!I-sil) A run was performed using the above modifications and the conditions of the last run of Chapter 2 (including the Kominz (1984) spreading-rate curve) Figure 48 shows the calculated weathering and reduction rates of reduced iron in clay minerals. Both curves are strongly influenced by the spreading-rate and C02 correction factors, and thus they show the general trend observed in most BLAG runs of a decrease in cycling rates from the Cretaceous to the Present. A comparison of the calculations of the modified model and the model of chapter 2 demonstrates a substantial effect from the inclusion of the iron cycle. The calculated burial rate of organic carbon (Figure 49) is considerably greater for the more complex model especially in earlier times. This is a consequence of the higher 02 levels generated by this model (Figure 50); higher 02 levels mean greater rates of weathering and oxidation of sedim:mtary CH20 so burial rates must be correspondingly greater to maintain the correct isotopic flux balance. The greater mass of 0 2 predicted by the model is produced by the incr. eased total production rate of 02 Conditions under which high cycling rates are achieved are also ones in which higher atmospheric masses of 02 and of C02 are able to be maintained. This general result was discussed in Chapter 1 as well, where it was shown that an increase in the burial rate of CH20 leads to a rise in 02 to a new, steady the system

PAGE 209

Figure 48. Results of modified BLAG model run with the Fe-silicate cycle showing the calculated weathering and burial/reduction rates of the ferrous-silicate reservoir.

PAGE 210

(_J z t-----l 0::: w I I-< w 3 z 0 t-----l Iu :J 0 w 0::: 0 (\J 0 0 (0 0 ro 0 (\J 194 /"'. (t: >(0 0 \../ w <

PAGE 211

Figure 49. Results of modified BLAG model run with the Fe-silicate cycle showing the calculated burial rate of organic C compared to the results of the similar run of Chapter 2 without the Fe cycle.

PAGE 212

w LL w ILL ::J 0 I I I-I-1-i 1--t 3 3 ( .....J A g 0 1 Is a 1 LU s t 0 1 ) :J :Jt!O .:l .::1 0 0 (\J 0 0 (0 0 m 0 196 0::: >-<0 0 ....-i '-/ w C) <(

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Figure 50. Results of modified SLAG model run with the Fe-silicate cycle showing the calculated atmospheric 02 mass compared to the results of the similar run of Chapter 2 without the Fe cycle.

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198 !""'. 0 Ct: >(() 0 ......... """-./ w w LL 0 L) (Q < w LL :J 0 I I ,.._.. 1-i 3 3 0 CD 0 CD CD N

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199 acts to balance the 02 fluxes but not to restore the reservoir masses to their original condition. Finally, Figure 51 shows the ratio of the burial fluxes of reduced to oxidized iron in clay minerals. The strong resemblance to the Kominz (1984) spreading-rate curve can be simply explained by a mathematical expression for this flux ratio: Ff,Feii/Ff,Feiii = [F0f,Feiifsr] I [F0f,Feii(1-fsr) + F0f,Feiii] (49) The ratio is thus only a function of f and two constants. This result sr is a reflection of the reasoning that went into the construction of the flux relations, namely, that in the presence of organic carbon, the reduction of iron in clays depends only on the temperature of burial, which is assumed to be indicated by the global seafloor spreading rate, and that it occurs at the expense of the ferric-clay reservoir. The Sediment Cycle and Carbon Isotopes cne of the least appealing aspects of nearly all long-term global cycling rrodels, including those presented in the previous chapters, is the treatment of the sedimentary reservoirs as single, horrogeneous boxes. The real system is obviously much rrore complex; either a continuum or a several-box approach with a range of time constants is certainly more realistic (cf. Southam and Hay, 1977; Sundquist, 1985). The comrron treatment is especially inadequate in the modeling of the isotopic cycles, where the sensi ti vi ty of the redox models is keenly felt. It is wholly unrealistic to assume that once a sedimentary unit is deposited its contribution to the mean isotopic composition of the entire reservoir, and to the weathering flux from that reservoir is simply proportional by mass to other units deposited long before.

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Figure 51. Results of modified BLAG model run with the Fe-silicate cycle showing the ratio of the burial rates of reduced and oxidized iron.

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0 0 (\J () 0 w OlJ (0< 0 CD 0 201

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202 A more satisfactory, long-term sediroontacy cycling rrodel needs to address the following: 1) the likelihood of recycling (erosion) of a unit as a function of its age; 2) the geographic locus of a unit's deposition, so that for example sediments deposited in shallow water during a transgression are more likely to be weathered during the ensuing regression than are deeper-water deposits; 3) tectonic effects, which may be cyclic (e.g. Fischer, 1984), including the development of rapidly subsiding marginal basins, and the folding of rocks which tends to decrease their area of exposure; Much effort has been directed towards a better representation and understanding of sedimentary cycles (e.g. Garrels and Mackenzie, 1971b; Veizer and Jansen, 1979; Dacey and Lerman, 1983; Veizer, 1984), but the application to comprehensive, geochemical cycling rrodels such as BLAG has not been made. A primary hindrance is the order of magnitude increase in computer memory required by this approach; this is by no means insurmountable but will require conversion of the modeling effort fr'Om micr'Oto mini-, mainframe, and super-computers. As a simple first step towards this end the isotopic composition of the weathering flux from carbonates has been recalculated based on a modification of the sedimentary cycling rrodel of Garrels and Mackenzie (1971b). Their rrodel was constructed to explain the apparent increase in preservation of pre-Carboniferous sedimentary rocks. Their hypothesis was that the tectonic folding associated with the formation of super-continent of Pangea during the late Paleozoic led to the

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203 protection of existing sediments; those deposited subsequentially were rrore likely to be eroded than those deposited before Pangea. The rrodel thus specifies the following: 1) the total depositional rate of sediments is constant in time; 2) post-Pangea sediments, divided into 50 my increments, weather with a half-life of 140 my (a value chosen to fit the expo-nential decrease in preserved sedimentary mass as a function of age); 3) pre-Pangea sediments weather without a specified half-life; instead they weather in proportion to their masses so that the sum of their fluxes is the difference between the total sedimentation rate and that provided by the weathering of post-Pangea sediments; 4) the total sedimentary mass is constant. In addition it is here specified that: 5) the total sedimentary mass is 25,000 X 1020 g ; 6) the depositional rate is constant at 58.6 X 1020g110 6yr so that the residenc e time of the sedimentary mass is the same as that in Garrels and Mackenzie (1971b); 7) the mean o13C of Precambrian carbonates is 1 .0 /00; the means of more recent sediments is estimated by averaging 50 my increments of the Phanerozoic carbon isotope record; 8) the carbonate w eathering flux is simply proportional to the overall sedimentary weathering flux. The calculated distributio n of sediments as a function of age is shown in Figure 52. Also plotted in this figure is Gregor's (1970) estimate of the Phanerozoic sedimentary mass distribution.

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Figure 52. The observed (Gregor, 1970) and calculated (according to the model described in the text) age distribution of the global Phanerozoic sedimentary mass.

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l I I r I f.-f.(f) f.(f) < r>-0::: < 0 I-['.. rn rz w \J 0:: f.-......... 0 ..J 0 w (..) w 0 w 1(f) 0 0:: (..) _j f.-< I I-I-0 I-r-I I I I I Ul 0 Ul (Y) (Y) (\J I I I I I I I I I I I I 0 Ul 0 (\J I I I I Ul 0 0 0 0 0 0 (\J 0 ow 0 0 Ul 0 0 (0 0 < 0 205

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206 Table 10 presents the average isotopic composition of the weathering flux from the carbonate reservoirs as a function of age. For example, the present-day o 1 3C of the carbonate weathering flux, which includes contributions of differing degrees from all earlier carbonates, is 1.46/00 During the late Cretaceous, Paleocene and Eocene it was 1.56/00 The entire post-Carboniferous shows very little change in the rooan o 13C reflecting the lack of an overall trend in the isotope curve for this period. This calculation is roorely a first attempt to better rrodel the sediment cycle and its influence on the global geochemical cycle. Future work will consider the detailed age distribution of carbonate rocks (Hay, 1985) for which additional information on their depositional environment is available. The exciting possibility is that given the extreroo sensi ti vi ty of the geochemical rrodel to the rooan o 1 3C of the carbonate reservoir it may be possible to better confine the excursions in the atmospheric 02 curve generated by the model.

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207 Table 10. Carbon Isotop i c Value of the Carbonate Weathering Flux Through Time Based on the Sediment Cycling Model Time Inter'Val o l3C Time Inter'Val o l3c (my B P ) ( 01 oo) (my B.P.) (Ofoo) 700-650 0.94 350-300 0.93 650-600 300-250 1.42 600-550 250-200 L44 550-500 0 17 200-150 1.49 500-450 0:00 150-100 L51 450-400 100-50 1 56 400-350 50-0 L46

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208 SUMMARY WITH EXTENSIONS The amount of oxygen in the is by the and of the global cycles of and Changes in 0 2 by an imbalance of the of of 0 2 that accompanies the deposition of in sediments and that of consumption the of the constituents. The cycle can be divided into two parts, an exogenic cycle and an endogenic cycle. The includes the of te and in clays, the biological synthesis and the of and the diagenetic, tion of pyrite. The endogenic cycle involves the ion of as is oxidized deeper and of 1 The exogenic cycle, dominated by the and cycles, was modeled in 1. The need a (few million year) time the of 0 2 consumption following an in 0 2 production was and met by assuming a dependence of the of CH20 and FeSz on the 02 level. The isotopic of oceanic o13C to a change in the depositional of CH2 0 was to the sluggish

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209 of that is a consequence of its long residence time. The coupled carbon-sulfur cycle was shown to react to a perturbation, namely the increase in the depositional rate of CH20, with a moderate change in atmospheric 02 and a balance in 0 2 fluxes within a few turnover periods of the atmospheric 0 2 reservoir. This balance was achieved without the establishment of total system steady-state; the net transfer of material between the oxidized and reduced reservoirs of both C and S continued long after the 0 2 level steadied. Summary of Chapter 2 The carbon and sulfur cycles were added to the BLAG global geochemical cycling model in Chapter 2. This addition allowed the calculation of atmospheric 0 2 and C02 oceanic compositions and pH, the rates of burial and erosion of sedimentary carbonates and silicates and the exchange of material during hydrothermal and metamorphic processes through the course of the last 100 million years. The model sensitivity to variations in the mean o13C of the carbonate reservoirs and to the gypsum depositional rate function was specific for each component of the system; in general those processes which are intimately involved with the redox cycle were particularly sensitive where as the others, especially those associated with the C02 cycle, were insensitive to these alterations. The calculated 02 atmospheric mass was found to be insensitive to modest variation in the specified rate constants of the roc>del but very sensitive to isotopic fractionation factors and mean o13C of the carbonate reservoirs. The model results were used in a speculative discussion of the global cycling conditions prior to and during the Neogene phosphogenic

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210 episodes. The Miocene Epoch was found to have notably high rates of organic carbon and pyrite sulfur burial, high global oceanic pH and higher than present atmospheric 02 A consideration of the paucity of Tertiary evaporites and the model calculations of oceanic pH suggest that ocean chemistry may have undergone a significant change through the Tertiary, culminating in the Miocene. Summary of Chapter 3 The endogenic part of the global redox cycle involves the oxidation of organic carbon (kerogen) by ferric iron, primarily in shales. This process can significantly affect both the quantity of organic matter that survives burial and the average Fen /Fein in sedimentary rocks. Thus an understanding of the Fe cycle is an important part of the characterization of the sedimentary redox cycle. An assesrnent of the sedimentary reservoirs and rrodern weathering rates of iron was made in Chapter 3 Excluding volcanic sediments there are roughly 900 X 10 18 (l'X)les of Fe III and 650 X 1018 of Fe II in sedimentary silicate minerals and 70 X 1018 rroles of Fe II in pyrite. The overall weathering rate of iron was estimated to be 9 7 X 1018 Because iron is nearly completely oxidized during weathering it is transported in the ferric state in streams. However, roughly 4.3 X 1o18mo1es Fe/10 6yr weather from the Fen reservoirs; the f th F III rema1nder comes rom e e reservo1r. The ferric iron in streams is in the form of ferric-clay minerals and oxyhydroxide coatings on grains. The latter generally account for 20-50 % of the total iron in stream sediments. Upon deposition, and in the presence of even a small arrount of organic matter, much of the

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211 "free" ferric oxides and part of the "lattice-held" iron will be reduced. During early diagenesis sulfate is also reduced, and pyrite forms. As burial temperatures increase so too does the mean Fe11!Fe 111 Therefore the redox ratio achieved before re-exposure and weathering is dependent on the temperature reached during the burial history of the sediment. The Fe11/Fe111 in preserved sedimentary rocks decreases through the course of Earth history. This trend either reflects an increase in the oxidizing capability of surficial processes due to the developllEnt of atmospheric 02 (a primary, evolutionary trend), or it reflects an increase in the metamorphic grade of the rock as it ages (a secondary trend); the latter appears to be the dominant effect. The Phanerozoic trend cannot be as easily discerned from available compilations of rock analyses. Thus an attempt was made to include the iron cycle in the Phanerozoic oxygen budget so that the Fe11/Fe 111 ratio could be modeled. A global material transfer reaction was constructed that specifies the proportions by which the oxidized and reduced C, S, and Fe reservoirs can change in mass without the production or consumption of atmospheric gases (02 and C02 ) or oceanic constituents. This approach was compared II III with another that calculated the Phanerozo1c Fe /Fe trend based on the average ratios for platforms and geosynclinal rocks and their relative proportions through time. The two approaches produced similar results, namely, a decrease in Fe111Fe111 through the Phanerozoic. Summary of Chapter 4 Chapter 4 presented two extensions of the model: the incorporation of the iron cycle, and a more detailed consideration of the carbon

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isotope weathering flux. 212 The present single-box rodel of the sedimentary reservoirs was found to be inadequate for both extensions. A preliminary set of Fe flux relations was added to the BLAG model of Chapter 2, and the model run under conditions otherwise identical to the last run of Chapter 2. The oxygen fluxes from the iron cycle were quite substantial; a comprehensive model of the global redox cycle must include them. The fact that the 11Bjori ty of iron reduction occurs during deep burial makes the process difficult to rodel under the existing framework. A several-box or a continuum model are the obvious solutions that will be pursued in the future. The sedimentary cycling rrodel of Garrels and Mackenzie ( 1971 b) was then applied to the weathering flux of carbon and its isotopes in a first attempt to improve the critical approximation of the mean o13C of the carbonate weathering flux through time A value of =1 .5 I 0 0 was found to be representative of the Mesozoic and Cenozoic FUrther confirmation of this value based on a more detailed rrodel will greatly increase the ability of the model to calculate 02 levels representative of past times. Future Considerations A number of lines of research need to be pursued to better our understanding of the global geochemical cycle. These include but are of course not limited to the following: 1) a quantitative description of the phosphorus cycle that includes the partitioning of nutrients between the marine and terrestrial systems; 2) a quantitative description of the strontium cycle, for which

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213 an excellent isotopic record exists; 3) a more detailed, multi-box or continuum model of the sedimentary reservoirs that includes the temporal effects of metamorphism; 4) continued addition of isotopic analyses to the age curves; an especially interesting period to concentrate on would be the Proterozoic/Phanerozoic transition (800-500rny); 5) the extension of BLAG over Phanerozoic time, Which will depend on the completion of the preceding, suggested tasks; 6) a consideration of paleogeographic effects on sites of deposition and climate; 7) a laboratory study of the relationship between iron diagenesis/metamorphism and organic carbon maturation; 8) the determination of the natural distribution of stable iron isotopes, and a consideration of the possible mechanisms of fractionation during geochemical cycling.

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214 REFERENCES Addison W E. and Shar'p, J .H., 1963 Redox behaviour of ir'on in hydt"oxylated silicates. In : Br'adley, W.F. (ed .), Pr'oc 11th Nat'l. Conf. Clays Clay Miner'; Per'gamon Pr'ess; OXfor'd, 368 Ahn, J .H. and Peacor', D.R., 1985. Transmission electr'on micr'oscopic study of diagenetic chlor'i te in Gulf Coast ar'gillaceous sediments. Clays Clay Miner' 33:228-236 Aliani, F 1983. Unter'suchungen sun Oxidationszustand des eisens in sedimentgesteinen als funktion der' zeit (Examination of the oxidation state of ir'on in sedimentary r'ocks as a function of time). PhD Disset"t Johannes Gutenbet"g-Universitat in Mainz Mainz; Get"many, 129 pp d 'Anglejan, B .F. and E.C. Smith 1973. Distribution tr'anspor't, and composition of suspended matter' in the St. Lawr'ence estuacy. can. J. Earth Sci. lQ: 1380-1396. Aoki, S Kohyama, N., and Sudo, T., 1974 An ir'on-r'ich montmor'illonite in a sediment core fr'om the nor'theastern Pacific. Deep Sea Res. 21:865-875. Arduino, E., Bat"ber'is, E., car'r'ar'o, F., and For'no M.G. 1984. Estimating t"elative ages fr'om ir'on-oxide/total t"atios of soils in the wester'n Po Valley, Italy. Geoderma. 33:39-52. Atlas, E. 1975. Phosphate Equili br'ia in Seawater' and Interstitial Water's Ph.D Disset"t., Ot"eg. State Univ 154 p Bagin V .I., Bagina, O.A., Bogdanov, Yu. A., Gendler', T.S., Lebedev A .I., Lisitisyn, and Pecher'skiy, D.M., 1975 Iron in the metallifet"ous sediments of the Bauer' Deep and East Pacific Rise. Tr'ans. Geokhim. 1 : 431-452 Balzer', w., 1982. On the distt"ibution of ir'on and manganese at the sediment/water' inter'face: ther'modynamic vet"sus kinetic contr'Ol. Geochim. Cosmochim. Acta 46 : 1153 -1161. Bathut"st, R.G.C., 1975 carbonate Sediments and their' Diagenesis. Elsevier', Amstet"dam, 658 p. Berger, W.H., Vincent, E., and Thier'stein, H.R., 1981. The deep-sea recor'd: major' steps in Cenozoic ocean evolution. SEPM Spec. Publ. 32:489-504

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215 Berner, R.A., 1962. Iron sulfides formed from aqueous solution at low temperatures and atmospheric pressure. J. Geol. 72:293-306. Berner, R.A., 1969. Migration of iron and sulfur within anaerobic sediments during early diagenesis. Amer. Jour. Sci. 267:19-42. Berner, R.A., 1971. Principles of Chemical Sedimentology. McGraw-Hill Book Co;, New York, 240 p. Berner, R .A., 1978. Iron: Abundance in rock forming minerals, I. Low temperature minerals. In: Wedepohl, K.H. (ed.), Handbook of Geochemistry, vol. II/3, Germany, 26-D-1. Berner, R.A., 1980. Early Diagenesis A Theoretical Approach, Princeton Univ. Press, New Jersey, 241 pp. Berner, R.A., 1982. Burial of organic carbon and pyrite sulfur in the modern ocean: its geological and enviromental significance. .Amer. Jour. Sci. 282:451-473. Berner, R.A., 1984. Sedimentary pyrite formation: An update. Geochim. Cosmochim. Acta 48:605-615. Berner, R.A. and Raiswell, R., 1983. Burial of organic carbon and pyrite sulfur in sediments over Phanerozoic time: A new theory. Geochim. Cosmochim. Acta 47:855-862. Berner, R.A., Lasaga, A.C. and Garrels, R.M., 1983. The carbonate"'-silicate geochemical cycle and its effect on atmospheric carbon dioxide over the past 100 million years. .Amer. Jour. Sci. 283:641-683. Boles, J.R. and Franks, S.G., 1979. Clay diagenesis in Wilcox sandstones of southwest Texas: implications of smectite diagenesis on sandstone cementation. Jour. Sed. Petrol. 49:55-70. Boyle, E .A. and Edmond, J .M. 1977. The mechanism of iron removal in estuaries. Geochim. Cosmochim. Acta Brass, G.W., 1976. The variation of the marine 87Sr/86Sr ratio during Phanerozoic time: interpretation using a flux model. Geochim. Cosmochim. Acta. 40:721-730. Burke, W.H., Denison, R.E., Hetherington, E.A., Koepnick, R.B., Nelson, H.F. and Otto, J.B., 1982. Variation of seawater 87Sr/86Sr throughout Phanerozoic time. Geol. 10:516-519. Burst, J .F., 1969. Diagenesis of Gulf Coast clayey sediments and its possible relation to petroleum migration. Amer. Assoc. Petrol. Geol. Bull. 53:73-93. Byrne, R.H. and Kester, D.R., 1976. and iron speciation in seawater. SOlubility of hydrous ferric oxide Mar. Chern.

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217 Curtis, C. D., 1967. Diagenetic iron minerals in some British carboniferous sediments. Geochim. Cosmochim. Acta Jl:2100-2123. Curtis, C.D. and Spears, D.A., 1968. The formation of sedimentary iron minerals. Econ. Geol. 63:257-270. Dacey, M.F. and Lerman, A., 1983. Sediment growth and aging as Markov chains; Jour. Geol. .2l: 573-590. Davison, W., 1979. Soluble inorganic ferrous complexes in natural waters. Geochim. Cosmochim. Acta 43:1693-1696. Davison, W., 1982. Transport of iron and maganese in relation to the shapes of their concentration-depth profiles. Hydrobiol. 92:463-471. Deines P., 1980. The isotopic composition of reduced organic carbon. In: Fritz, P and Fontes, J.C. (eds.), Handbook of Enviromental Isotope Geochemistry, Vol. 1. Elsevier, Amsterdam, p. 329-406. Desprairies, A., 1983. Relation entre le parametre b des srrectites et leur contenu en fer et magnesium. Application a 1 'etude des sediments. Clay Min. Drever, J .I., 1971a. Chemical weathering in a subtropical igneous terrain, Rio Ameca, Mexico. J. Sed Petrol. 41:951-961. Drever', J. I., 1971 b. Early diagenesis of clay minerals, Rio Ameca basin, Mexico. J. Sed. Petr'ol. 41:982-994. Duinker' J.C., 1981. Par'tition of Fe, Mn, Al, K, Mg, Cu and Zn between par'ticulate organic matter' and minerals, and its dependence on total concentr'ations of suspended matter. Spec. Publs. Int. Ass. Sediment. 5:451-459. Dunoyer' de Segonzac, G, 1969. Passage au metamorphisme. Les miner"aux argileux dans la diagenese. Ph.D. Thesis, Univ. of Strasbour'g, 317 Dunoyer' de Segonzac, G., 1970. The transformation of clay minerals during diagenesis and low-gr"ade metamorphism: A r"eview. Sedimentol. 15:281-346. 1980. Alkali cation selectivity and fixation by clay Eber'l, D., minerals. Clays Clay Miner'. 28:161-172. Eckel, E .C., 1904. roofing slates. On the chemical composition of Amer'ican shales and Jour. Geol. 12:25-29 Eckert, J .M. and Sholkovitz, E.R., 1976. The flocculation of ir'on, aluminum and humates fr'om r'iver' water by electr'olytes. Geochim. Cosmochim. Acta 40: 847-848 Ehr'lich, H.L., 1972. Iron, oxidation and reduction -micr'obial. In:

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218 Fair-br-idge, R. W. ( ed. ) The Encylopedia of Geochemistr-y and Envir-onmental Sciences, Dowden, Hutchinson and Ross, Inc., Pennsyl. 1321 pp. El Wakeel, S.K. and Riley, J.P., 1961. Chemical and miner-alogical studies of deep-sea sediments. Geochim. Cosrrochim. Acta 25:110-146. Elder-field, H. and Gr-eaves, M.J., 1981. Str-ontium isotope geochemistr-y of Iceland geothemal systems and implications for-seawater chemistr-y. Geochim. Cosmochim. Acta. 45:2201-2212. Emiliani, C., 1955. Pleistocene temper-atur-es. Jour-. Geol. 63:538-578. Eslinger-, E., Highsmith, P., Alber-s, D. and deMayo, B., 1979. Role of ir-on r-eduction in the conver-sion ofsmectite to illite in bentonites in the Distur-bed Belt, Montana. Clays Clay Min. 27:327-338 Fanning, D.S. and Jackson, M.L., 1966. Clay miner-al weather-ing in souther-n Wisconsin soils developed in loess and in shale-der-ived till. In: Br-adley, W.F. and Bailey, S.W. (eds.), Pr-oc. 13th Nat'l. Conf. Clays Clay Miner-als Per-gamon Pr-ess, Oxfor-d, 449 pp. Fischer-, A.G., 1963. Essay r-eview of descr-iptive paleoclimatology. Amer-. Jour-. Sci. 261 :281-293. Fischer-, A.G., 1984. The two Phaner-ozoic super-cycles. In: Ber-ggr-en, W.A. and van Couver-ing, J.A. (eds .), Catastr-ophes and Ear-th Histor-y. Pr-inceton Univ. Pr-ess, New Jer-sey, p. 1 29-150 Foster-, M.D., 1962 Inter-pr-etation of the composition and a classification of the chlor-i tes. United States Geol Sur'V. Pr-of. Paper414-A, 33 pp. Fox, L .E., 1984. The relationship between dissolved humic acids and soluble ir-on in estuar-ies Geochim. Cosmochim. Acta 48:879-884 Fox, L E. and Wofsy, S C., 1983. Kinetics of r-emoval of ir-on colloids fr-om estuar-ies. Geochim. Cosmochim. Acta 47:211-216. Fr-oelich, P.N., Bender-, M.L., Luedtke, N .A., Heath, G.R. and DeVr-ies, T. 1982. The mar'ine phosphorus cycle. Amer-. Jour-. Sci. 282: 474-511 Gar-r-els, R.M., 1984. Montmor-illonite/illite stability diagrams. Clays Clay Min. 32:161-166. Gar-r-els, R.M. Equilibr-ia and Chr-ist, C.L., 1965. Solutions, Miner-als, Fr-eeman, Cooper-& Co., San Fr-ancisco, 450 pp. and Gar-r-els, R .M. and Mackenzie, F.T., 1971a. Evolution of Sedimentar-y Rocks. W.W. Nor-ton and Co., New Yor-k, 397 p. Gar-r-els, R.M. and Mackenzie F.T., 1971b. Gr-egor-'s denudation of the continents. Natur-e. 231:382 -383.

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219 Garrels, R.M. and Perry, E.A. Jr., 1974. Cycling of carbon, sulfur, and oxygen through geologic time. In: Goldberg, E.D. (ed.), The Sea, Vol. 5. New York, Wiley Interscience, p. 303-336 Garrels, R.M., Lerman, A. and Mackenzie, F.T., 1976. atmospheric 02 and co2 : past, present, and future 63:306 -315. Controls of .Amer. Scient. Garrels, R.M. and Berner, R.A., 1983. The global carbonate-silicate sedimentary system --some feedback relations. In Westbroek, P. and DeJong, E.W., (eds.), Biomineralization and Biological Metal Accumulation. Dordrecht, Holland, D. Reidel Publishing Co., p. 73-87. Garrels, R.M. and Lerman, A., 1981. Phanerozoic cycles of sedimentary carbon and sulfur. Acad. Sci. 78:4652-4656. Garrels, R.M. and Lerman, A., 1984. Coupling of sedimentary sulfur and c arbon cycles-an improved model. Amer. Jour. Sci. 284:989-1007. Gear, C.W., 1971. Numerical Initial Value Problems in Ordinary Differential Equations. N.J., Prentice-Hall, Inc., p.15B-166. Goldberg, E.D., 1952. Iron assimilation by marine diatoms. Biol. Bull. 102:243...:248. Goldich, S.S., 1938. A study in rock weathering. Jour. Geol. 46:17-58. Gregor, B., 1970. Denudation of the continents. Nature. 228:273-275. Grieve, I.e., 1985. Annual losses of iron from moorland soils and their relation to free iron contents. Jour. Soil Sci. 36:307-312 Griffin, J.J., Windom, H. and Goldberg, E.D., 1968. The distribution of clay minerals in the world Ocean. Deep-Sea Res. 12:433-459. Hachey, D.L., Blais, J.-c., and Klein, P.D., 1980. High precision isotopic ratio analysis of volatile metal chelates. Anal. Chern. 52:1131-1135. Hay, w.w., 1985. Potential errors in estimates of carbonate rock accumulating through geologic time. In: Sundquist, E.T. and Broecker, w.s. (eds.), The Carbon Cycle and Atmospheric C02 : Natural Variations Archean to Present. .Amer. Geophys. Union. Washington, D.C., p.573-5B3. Heller, P.L. and Angevine, C.L., 1985. Sea-level cycles during the growth of Atlantic-type oceans. Earth Plan. Sci. Lett. 75:417-426 Hem, J.D. and W.H. Cropper 1959. Survey of ferrous-ferric chemical equilibria and redox potentials. United States Geol. Surv. Water-Supply Paper 1459-A:1-31.

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230 APPENDIX 1 MODIFIED BLAG FORTRAN IV COMPUTER PROGRAM The following pages contain the main program, the differential equation subroutine (constructed after Table 4), and the initiation program used to run the comprehensive geochemical cycling model. The program uses the implicit, multi-value, finite difference subroutine DIFSUB of Gear (1971) to integrate the set of differential equations in the subroutine DIFSUP. The program is written in Fortran IV and is in double precision. Notes appear throughout the program as documentation for particular calculations. The run is initiated by first creating a file, INIVAL.LK6 that contains the initial values of the run. Only the dolomite, calcite organic C, pyrite and gypsum S sedimentary reservoir sizes and isotopic need to be specified. The others are calculated by running INITSS. After INITSS i s run, SUPIMP is run, and the requested model supplied. Usual value s for these parameters are: EPS=. 01 H=. 001 HMIN=.0000001, HMAX=.1, MAXDER=6, MF= 2 The model then runs for approximately 10 minutes on a PDP-11 mini-computer, from 100 my to the present. The calculated present-day conditions are then compared to the expected values and the initial conditions corrected accordingly. INITSS is then re-run and is followed by another run of SUPIMP. This sequence is continued until the present-day conditions are matched to an acceptable level. This generally takes three to six or so iterations.

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, ' ... ... ,., .. J. 231 A version or 8LRG1 to et a l t h a t c a 1 c u 1 a t e s t ,., t lu :-; e s a , d r-e = 2 r-..-c :.. T' ; .: ,:; ;, Cl t" i"h? s lobal :3eochef!tlcal J.i.clujll;s t.;1>? : .:::cl?:; o-:C a :-1 d S 1 t u s e 5 a t a i o r e o v e r = 1 .:-, r: c., r !..1 l .. u fi of (IY/1) to 1ntesrate the set G f e a u a t 1 o n :; o f t h e s u b r o J t 1 r e Ll 1 ; -::; u t-' double Precl S lOnt fortran 4. .l t ::. s run j,, N S o 111 e r 1. J 111 b e r s w ri 1 c ;, w ? r e d o u ;, l e ::--r e c r1 a v been shortened for text' e .:3. is now IMPLiC i T KlA L* 8 (A-H,U-ZJ COMM U N 1 COM MUN 1 i,; u M M UN I ':' f' b:l '( t-'1-\ 1 :i I i-' t: 1 J H i t'l 4 H' 1-\ 1 ::i ; Y i-' R 1 b Y is ffiatrl x cr aGd 1 s u x the of reservo1rs YMAX l5 the or each reservo1 r and 1 s uPdated r i l e at, {-p;:-r f1l a t r J. e 5 a .. e t' J. !""i aj l ,-. e a f' { : .,. / ;, DlMtNSlUN 1.1 Hl t:. N ::i 1 lJ N A .; C:! ) 1' t: t-: I' 1 t / 2 1 ) 1 Y F n ( i. .:, 1 ) 1:: ( 4 ; i...: U 1-( 4 ; N :t. :. numt1e \'\ of r r v u 1 s :::) i t..i-' !_,;,e :.:.. :--1 nt ::, 1 :l 1"11.::-r ::'f12 1"1 t, J 3rt oj f' i i t 8 ): i;. i "11? 1 aS t t liT!(? ( l C I l l ':; i N =--11 , .. ..... -== en t. e r !i: .:. :: .j t:: r 1 .-. r a c c e P t .,: IT a : : T ' o 'I' !:, _t :=e :,: ? ,:;, s H t H t-'l l ., \ l'!t ., i ... :) :;; := e :,:, ::' Ka::. '!' 1 :-.: s 1 \ : .; a c c: e r-t. .;.: L <:: "' 1 f \ o a :J r e 1 > o i ._: 1. i-U 1 : ri H 1 \ LU v 1 ::; )

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c CJ f' 1:. N ( u N 1 I = ::: l y j-' 1:-. :: u L N (!lV I t-_ :: ; .:. N l \,.' A L 6 C LOSEtUNil=:::) fYPE *' BA CK KUN1 T *, l Y t 1, 1 i, 1 = 1, 1 6 J { 1'' 1 X 0: :::: J = r ( 1 1 ::: ) o: : 5 i = Y t 1, r ii H X \ 4 J = "1' \ 1 ) r i"H1X \ !::J):::: r \ 1, 5) 1 ,j' > Y i'lr:i X \ ::3 ) ::: { \ 1 1 E ) YM;';X ( 'i) = Y ; l 1 ;.) Y M A X ( 1 0 .i = ( ( 1 1 0 J :;.1 > = t 1, ::.11 \1 1 :':1) Y i'i ,::, X : 1 {;, ) "' t ; l Y .;) j 1n1t1al 232 03 1s del D4 1 s del and are the1r :Lnltla.L o r 1.13=:1"::1+ l:::::iOOLIOO :::). Ji.JOOLIOO :::: (.) + 0 () 0 i.) Ll 0 () X :: 0 v o v :_ Li J ; ) NC;::,L.==O L..:. :'l ii H : _, I :, :-.. : -::. r :\J E r 1 :-, : .. : t.. t r 1 ... j t t. 1 rr! :? ; t i:. X 1 .,. X 1 I ;:;. I L :' :N: ::: o:: n :.; n 2 l' t:: s u s -:1 J. :? . .... n. I:.,.''

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c:: 100 10 1 ::: 1 0 0 0 v U .U v -X J = = 1 N r 1 ; c Calculate the P H CHP) c Write the results to a flle 125 1 : 5 F U h: f A I t ;-!:i 0 l X '/ , 1 )'. ::) 1 X 1 "2 t t/ 'J. ) ) (f(l,L J,L=l L6J 138 0,4,1X), c c L Iii r 1 t >:> t. o t h ,::.:;i "!l: ;_;-:_ T=lOO.OUODUO-X .. c c c f.! ij H li 0 = L i tJ l.! :.: G .q u = ;,.; : 3 !-\ 1.: 4 i :. l F t" 4> L t:: 7 \:) U ) L i l j t\ t-1 V ,;,; ., / '/ b .I ; / :.5 L! :_i 11-t l ij 1 / ::: U AN Ll I Lt. 1 : ) ; U i:, l"\ ,:., :_: :: i: v 'i 7 / i...i 1 J. '>' J f: C. T G l 1 6 :5 N .Li ., f t L. t V .:; : l } Li '.:.1 ;..: i::, :. : :.-: \.: ; .. .. '7 .,:, .:. b o 1 f-" ( l u : 4 (; ,: . F t Nil I L :t .::, 0 i..i :.:i !"\ f:; :_1::: ; .::. 4 l :;. ::i : ; I F \ f G <"-l .:; ;J , :\ N i.i f L t:: :;-j l .. 1.) ; 1 1 : j r: Pi i.l ::: ;j :::.i 6 6 0 j / I .3 ::_, :-3 .L F ( 1 lj :::. 1 N Ll i L. ::i .) ; Li :j : ; f:l JJ " : .) () V v ;J .) 1 F ( ; d i 1 :::; t_.; Ft N i i 1 L. t:: ( .l ::. ; > j r.: .. i.1 :::: .i . .:. 1 t.-:; :; t / 4 l ::. 1 -= U l' ... : ::: i-., N U i :... ;::. + / ::. ) iJ _:; ; : ,_::::: .... < iJ i...; ,5 / 6 I :i ,.:. 0 '7 / 233 i {-\ 'f' ij I l + ;; NV i' l .. ::1i \.i 0 ) lJ lj i : F1 :, : ::: .. -:j .:. '-/6 ... ';-' 6 : -:: 'i l .. ( ., U : t) u N ll I i_ 6 ,. 'J 0 ;,it::; .. /-1L! _-:: ':. :J t; :.: t; .i F ;; i u r :; 6 v t-HH r u: : ;. .. >i ;;. .; i.:i ;..: ;::; .. = = 1 1 .: :.:; \ ; \.l v o J. ;:.-i t :_] f t:: li :' 1 r i :.1 L t:. l / \) ) ll \J i ... : A V = ... 0 / :, / / / . / / I I :' / .L ;-( 1 1' !J : l / \, r:, N iJ ... I t L!:. 4 V i j ; U l:i t\ A iJ = .. lJ 7 I.:; a:.! 6 0 0 ""'. . : : ;

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c L; c L: .. .J r ... G 1..; L: c c I '' L; : .. L ; ,_; L: c t.; (; L ; .... .... l : c; t.: .... t_; L I .r t.; .... t.: ,,, c c c c t.: i..; I ... t:: L t: i ,; I' \J 1Fti ,Gf.4U.U.ANU. ( T G T 4 6 t 0 t AN ll I t L 1:. :.:1 1 :.; ; Ll ij i:; L : == .. t iJ ::.. 0 1 ) i .1 1 F ( T G r S 1 0 A N (I ;' L t:: :j 1 :.; ; J t j ,4 L ::: 0 ij v i) 0 (i 234 I 1: ( T G 1 / U A N i.1 I Lt. 6 .j (.: i !.:i i, L:::. \.: :.::: .:.. . .;. ..:. .,: .5 ..;. ,:. ..; . _s :, ..:., J .:.. ::1 J: F < G r 6 J o N i.t !' L t: 1.:. o ; :.. j h : A u = : j ::. :::.:So / 1 .; .s ;j 1 o :-.!.;;. I F ( T !.J T / 6 0 AN ll I L 1:. t (:! ';' 0 I :.'. j h: ll = \.i l i .) () I 6 ..: ::: .:, iJ I .:, 'i :.;. J. r ( i .. L; ( 0 t ij A N i.l r + L [ i t 0 ) v u ? i =-+ :2 ::; : r I .:.: ::; :::; / l .... .. d ::,, / 1 .. 1 : : c, I u T ''/ 6 v A tJ ll I Lt. 1 0 4 j :..t tj r : t:1 Ll = 'i .:.. /::; \. (; \J I F <. l G i' 9 6 0 A N it I t_ 1 ij 4 ;o i.i U : : Fi .;.; :::: 'J i j i j i i i ) IJI? 1 c !F(f ,GE.O UU.ANU. I .GT.l,UU.A ND. I 11-(l.GT / oOO.ANU. I IF(T. G l Y .UU.ANU, I 11::( f b f 1 U U A N ll 1 L t: t.> j ) IF< I G i .16.0.ANLI i L:: l'i.O> Lib kAL!4:=:, ... :.:::1 oo LILH\ AJJ4=, '1.:::0000 i.tlikAi.t4-==0, 0 000 J ) :.:i r: A Lt 4 = ..; o v o o lll.:.i h A lt 4 = :.::: ',;!. :::i 0 v 0 t fa \ f + U l :.:!. V + 0 { ; N 1J I L t:" .,:. :t ,. ; J t.:.i t:d.J 4 = ... :. -:) C V <) I ;: \ f li f 1 :J . ::. N L1 f t L. t. 1 .. .-::.!. 0 ; ;) U q v 4 = o .. !""; V 0 C IF ( T t ij I + {j t (j I; N Ll .. :_ (o t :.:, ; ;J ij ;:..: 1.1 -:-;. =: '.j :J b t 6 t -:;, t,. ;:;, 6 6 6 6 6 6/ l F l i' ti i' ;:.: 1 :) AN J..i f L C: ::. ;:.1 J U li i : !=i :.: 4 = .::, ,-;, 6 6 .= :; : . s 6 6 -:> 6 6 7 1 r \ 1 ti 1 ::: 1 A N Lt .. 1 i :: ::::. i ;_; 1..:. ,,. H JJ = ] : i c o 1. r-< r u r :;: :.::: u A N u r L ::: . : j .i ) v t:: r.: .; v l = o ;: ;,:, u eo ;J o 1 F <. T l.:i I t-j 0 t-"i N Ll 'l cL l:. 4 C ; :.: t: !"'.' ::; U 4::: c-::.;. ::,. {, V 0 0 0 IF(f,Gfo24.U,ANU. ( j l:i I' :.::: d v AN lt I L l:. .!>;:: J ) i.i t: !..1 : : : : 1 :,; :.) r,; 0 0 1 f ( i ., !3 i 3:.0: J {;\ N ll 1 1 ... (:: :f., 't .l U lj < ,:: U .::; ;: 1 / J ::. ( J ( .l i-( 'l ij f .... 6 '1 : J A N U L l : ..:;. ':1 .J 1..1 ;_..; ;.J .. 1 0 0 0 0 1 ;:. .. Z r + LJ f 0 f t N U l.. :::. .:, :) / Li ij o"': i:.:i U .4 : : i 0 :dj 0 (_; 'J 0 .ll .. ( -:l j i : j . Nit .. ... i_ C t; ::! I t: .! .!..1 _ ; I _\.; ...::; ; : ';_ ...... :: .. .. ........ .:. ..: :. .:. :3 .. II:\. i + !j r i 4 .._. (j. ::)NU. 'I' Lt:.. -.; i ': L .. ; = ... i .. t;.:-o:' L i-t. i + b i 4 4 ;..) Ll < L i::. -; C. :; j _:,:, ._: ..::: :: .J .J t.J _: 1: : .. ( r ; u 1 = .. 0 (.; u ,- i _ c o J ; ; :: : .:: : : . :;: ; .l F \. I liT ::.::;, (J :.1 N J) . . -. 1 ) a ... t .' I C .,.. f',.t_i )::..'/ .,C :_i < L.i. .,. 6 : i ( : ; + + ) = j : i :: ..... 'i .:. :.; 1.) :; : : .: r=1 L ;.:; ., .: :::. ._ "v.: : 1 f ( i G l S "'i 0 N l.: L :. t.. ::: : iJ : L :.:: !" { o : > : ::. .. (: '.' \ J F ( T t3 i ., :3 + + ;\! l.l + 1... .:;. t' 0 U j ,: i ..i ::: ,. !. ) .. : .) :.; .:) l ; .. t. + iJ 1 *' 6'-; f::j i\l U .. L b ..... ; J + ) .' :.:t: ; :< u "+-:- .. ; :-_, ... ',.' .... iJ J: i:: ( i tj f 7 i.) + 0 tJ. i: I' I :... i ,. ? : .. ; . : L i ;j :) i ] (:. 0 . :..) 1 r-( c i:-1 / :L + o . :..i + : L l : v :) : ... ;:., ,J 4 ::-.: : . "': o ) :; .t F { f G f .'' ..:: + '..) .. ;.) 1 1 f L / 4 D ;. 1 ,-:, U :: \...' : j .' j l : -'": .. b i ./ 4 t U 1 > 1 V I L i: . l : . \.J } __ : .:! !-.; 1 : ::: ... ::.; ;:--_, ; i ) (, :i I F {. f G f .? 0 N Li :' .. \... :0:: -:: J \; J U i j ;-.: i J 'i = ....... J :; :... : / 1 F { I ( li T + i:1 u :; . -:lN.:..! I A Lt .... : 3 '1 .. 0 j ll i j ,.; ;; iJ :-:: c : fJ :.; oJ :) ,_. i F t .;,1-t U 'f H li AN Li .. : L t or U i ,J :_i 1 : { ; t: :;. :: : j l: :..i ..

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L c (; c c . '" c I f l i j I' 8 'i U c=i f'.i L l l L !:. 1J < ) ) 1.! :_:: :..; A V 4 = 1 6 0 U v v I F ( T G 'f 7 1 U A N J..l I' L L 't 0 i [I L; r.: A 1.1 4 = / J v 0 (; <) I F ( T tn 'i '2 U A N Ll I :.. i:. ''I .5 i j ; i.l j f \ r-, J..! 4 = :.: ::.; (; U \i \i IF Ltt,; :-: ;:, ; J '-l ==.. U :: ::J U U U v { J 1 F ( I li f , 0 r:l N ll : L .l 0 ) L1 i'\ A ;_; 4 .:: .. 1 /)I) iJ t l 0 I F ( ') u 1 1 :5 o AN L! : L t-_ 1 'I' o \ l lli 1 '\ f 1 U 4 ::: .. 1.1 ,'j 1 6 6 t;, 6 :,') .::, 6 6 6 6 6 6 ,'J 6 J: F ( I I' 1 Y v A N ll T' L L 6 U ; J. F i. 'f ; :.: 6 U A N i.! : L 1: j 'l 0 ) .lf( I.Gi J.q, O ,ANLI. u r .qu.o. A N u 1 .Lt.46.u> .( F ( i l 4 6 U c=i N i.l i' L t:: 1 U j 11-( 'i l:i j' !;:; 1 i) A!-( !.1 i :... 1 :. '::. I U ) J. i-' t I G i' ::, / r 1 .LI I' !_ , ll l L1 U Ll 4 ::: ( ) / j i 1 4 ,: :3 / l q :.:.: :.:".i i ll i.:i :_t 4 = 0 1 I :-;, () U :.; r-: A Ll < l : : U .:S v U () i.l F Li 4:: 0 U !, .,5 .l ) 3 .S j J ; .,5 .\.! L: i: A Ll 4 ::+ 1 U 0 v :; U U A U 4 :: t !3 1 6 C > .; 6 !: .) -; .. !, 1 r ; lj i t. d v h N Li ; L i:. ( o c : t """; ;r u u t.: A LPl = ..J v .1: ::: i li i ; .::. :-3 o N L r L c: / <+ v > .\.i l:! b' A JJ4 :: - c:: 1 i) u o .lt-i. t' ,. G i I 4 U AN L1 : ,, i_ !: o 'J ij i i.i l:i t': A U 4 = 0..::: v U ;J 0 o 1 F i u i' d U 0 A i\C .L.i : L : : i:i 4 U ) i.i i_i r-.: ti l i 4 = U 'L:.:.. : : i 0 0 .l ( I b : d : 0 A r llJ : L i:. o 'I !; ; i_: ::. t-: Li 4 = 0 0 .l \ 1 .1. t=' ( i' G l 'i 0 A N !.1 i U:: '7' 6 v .Li ; j i '\ U 4 .:: 0 , ; ::: d ,: : / 1 .1\ ,: :.:;: ::; / 1 .. !l .:1 .l \ . l.j I + 'i /;,. + u f.1 N .. ; .. -i: l 0 t v I .\.: t j 4 :: .... :t ::..: : 7 .( F \ I !3 f' 6 U A N l l f L. J. 0 -'1 \J ; .l.l b ;.; A i.i l : : i) \i 0 v 0 u=-=v. OvUvOULi O N C 1-H_ : c i { L ri L i 1 i\ 0 == _';1, ... -. . c:; .. .... : \. 5o > r r 1 e c 3 .;. 1 t :... t.. i-: . :.,; r:. E' 1 ,::" .: , : .:.:.. t : .i ... ., J .;: l ;.. : i -:1 n 1 t 1? tj 1 -; = r 2 :--:2 t2 r :: .. -:-.. :... ; .:::. ... :-; ;.., 1 / : cALL Li r :,:; u r: { N 1 i< : ,. : : ; v t.. : ; I ,. i ; r'\ i ,' 1 ; : : ;i ;\ t : :. r=-, .-: : 1. Y MAX t:. i': :_: r: 1 1 \ t'L ; i_:: 1 "': ; f.. i .. .:..r L '= : :

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c: c t: c ('' c (' c . ... c \,: l . kflas is an error 1nd1cator !F r ::,:; 2 r r e s e r v o 1 r -::. ; 1 z. : > 11 1 ..... ; i c:; r c_, f'. C4 L c c;: c. :.: l a t t-:: ::1 1n tne routln& lYP l (1tl9l)r i=ll6J Ulfl=1{lyl )-1UU0 it 1-' ,: = y ( l t ; ) . 1. oi::o, = t t 1, :-J) -:.::::..o. .1. f 1..; ;:; :=: L11 t-' 1 > i:: r J. o (J uJ ( j j :_; i J r u 1. v 1 o 236

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lUlO 1 !-=" Ll A t< S l i.l 1!-; G I ::! .;;(HJ ll 0 U i I F ( D A tt S ( (I l C: i 1i I 1 U 0 0 ;_1 v {) i fORMAfl/,' CLU::il: liJNll ::;::: ) ::i GU I U 1010 l:iU ru 1 0 lt) :.;u IU 1 0 1 0 G U ru 1 v 1 t ) = lX ll::; > l UN! i =2 i > tYt1,1lrl=lr: 6> t ( 1 8 > = Y ( l > Ll i F :3 E W HW :.: R l 1 L < 2 ::i ) ( Y i 1 1 .( > r f :." 1 1 .s i C L u;;t: l U N 1 IPL l THEN lvi::i sruf ENLI 237

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c ('' \ c .... .. .. . I M f L l C ll r: c. Au: 8 A I; l ; COMMUN c 0 M M 0 N i ll t: L i' f) K I ;II :-(:A F : 'lli 1 (: I: s l 1 ;-J ? 1 1 1 l 4 r: t-W Ll U L 1-,:, v 1t. A K I' K 1:'. 238 COMMUN 1 fh1s suDrout1ne conta1ns tha dlfferentlal that are solved the C61 1 to C02 1 s the rat1o or curren t i'll'.' \.,-'-J ... to present valG 8 FB 1s the weather1nS rate correct1on factor lU 1 s 1n lO=X+H 0 = 1 : 1 I:O=i'\lt l 1s the land area r a ctor et .l F-t. I () L f .:, 0 6 0 j 1 .. A ::: o 0 ll 0 i \..i U U I 1 o 'i :1 0 Li 0 ;n 0 IF( IUobL.4U.UU ) lF' f : (. 1 G t:.: / : .:: 0 .r r :-i :: .., / : :: :.) : : Ll L : t. l t1 t c v ... 1 c ;r .-:, :; ... ::.. "J j :_: : ) )-,:. :_ .:: .... == ....... :. ..: t.. .j .:. .( r u L f. \. r t ... '.:i:.:: .. ;j :.t v ; ... ::: 1 .; ... '") L .... '/1 1 f: ( T () o l.. I o J. ij V ) :::: ; .. ; :;:: 1 + / .) V \i il () !::)UU;:-ir'll"l I F i" U L:i L 6 d u > F ::, 1 ..... \; li :::5 c: J 1 () l \ I 0 r t : : l:. i; i r h :: '" :""; a J J \ C ; i ;=-( f ij t:.i t: 7 t t: ) ; : i'\ :-: M ..:, ., l :f. ;') t. f { ).L'I ... r :.;;:\= -:.. :.:.,:; ... tJ.\:t: ; c .i. f ( i v u t. o > r :j == ... ... \) v :.: : :. t-= \ u ,_; t. : u o > 1 :1 = 1 ..:. ..,, 1 :; t.

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c (" c: i. I () l3 1:. .1 ::.i 0 ) f S 1\ = 1 ::1 :) J :.:.: :?: :: .. I F < 1 0 u t: 0 ) t-" :::; k = 1 4-, .i ;j o ;r. i" 0 IF .-::; :..: = c; ::.-.1. f ( 1 <.> l:i t 6 :.; o J t-r: : = ::_, .,.. :- v u 4 : .l F t i 0 G t: I 0 U ;. t-. ::H :.::: I .S + The corrected rata constant3 C u 1: = F-r:; ::t: I l.l CWU=. UUlYoUUU*CUR ewe::::. utr i.; l !, :::.:i + J 8 2 ,LIU : : : 1_: U f FWCA=:.:!.):.:!UUO#COk FWMl:i==..l, 02:J LiO;;-
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240 c on the run cond1tions, c dePos rate c f32= F.320 c c c ("' c t.: c c .... c c .... '-c ..: c c c 1 1 1 :i. 1 :t ... 1 I F < T 0 G 0 0 ) t-" .L! = o ::i o v v v i) ll 0 11-( r o G l o o > F .5:.:: = o ::; o o (.; o o Li <; .1. F ( i 0 G r 8 0 {) AN lt l 0 L 1 'i 0 Ci v ;; F = ..5 o 0 0 oLIO lF( 1 F \ I 0 G l :::) 0 rJ ) I 3 :: r r t. A 1\ f32=1.000 Calculate the sulfur1c ac1d weathering fluxes fFMG=F 1.5)1:1-MG ff lt=t1 J:H f.t FH;A=I-l .ili-Cfi f : FL= F 1.5:ct1 I ) f. (_: ( j .:.; oJ (j Ll () .[ i' t ;-i e m a 1 1 e r r e c t 1:i t :) f... r. , : )! .., ; : ::; J. s 1 ; ; .::: i 'J d 2 1 t 1"1 e rout1ne mas not comPlete t-4 !.:1:: : llu r : A ;_; 4 _.: Y <. 1 :::. I ::.: 4:.: Y <. 1 l 4 i --;_: ; ; ..:, l ; ( J. : i -Li i / ::: 0 0 v ll U t-. W U u L ( "( t v l I ; J :; i ; :'( '. (_l :i i) Li '..; 1 1 s e a r ? t, he tj 1 t e r-e r. t 1 a 1 2 .... :., .., .:.. ;! 5 w t h c.; . J l.. calc1te fJeP':'slt.J tt r, .::.i t .. =:; ;:-: : ... =:> F c c w h e r ? i t 1 s a s :. a_; 1T1 e.-;:.; t n .; t. -:-, ; .o: 0 c <:: n ma1nta1ns saturat1on Y F' k 4 = F W L1 i-F t t I W C IJ:::i W 1 r i H 2 0 0 0 0 1.1 iJ ;:j< t-F L: + t-1: :_; A r: ::> + r: : .. .:> ;.:-: v C 0 Li (.i :.'< i-.;) l Y I J "" 4 0 0 L1 <; iJHi t-:.: v e 0 U :y* : W t>l<;; ;;< \ .i C Ll Z: : i,.JL; Y ( 1 6 j MY l l '!.J) tHlJ4):f.f(l>:J))

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c c c The coruPlete set of d1fferent1a1 eauat1ons note that onls the r1rst 11 are solved (see d1scuss1on in rua1n 'r' F' 1 M l l 8 1 ) = F 3 1 I. 1 3 YPklMEClO,l)= Yf-'klMt.( 11' 1 J=-t Y l 't\lMll C:' l ; t Y i 'KiMI::.t'/, 1)) YPk1Mltl6,l)=U,00UUU0 'lnese are TJrartst;:,..rej tc tl.e nta:t.r t c,; ter has been ach1evad YPK1J=YPklMl( l J,ll L fUr: H E.NU 241

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c c c c c c c: This Prosraru calculates tne steadY state 1n1t1al conditions ror raPldlY reservo1rs IMPLIC I I (A-HtU-L> BYit:: I ..:IJK\.11:::<1) 242 1.1 l1' t. N !:> l 0 N .B ( 4 ) l:l 0 ( 4 i C U 1-i. 4 j X (J U I l .5 ) i"\ Ll U I l { j i r ( !:l 1 1 b ) U K M A l i. L1 ,H) 1 8 j Read the old 1n1tial values' wh1cn 1nclude the 1n1tia1 values or the sedlruentary reservo1rs that w111 be u sed here CJ 1-' N ( IJ N 1 I = 2 "f'i 1-' 1:. = U L L1 M t:: = ; 1 N L V A L L K b (Yllv 1)tl=l,16> CLU::ii:.( Read the gyp dePo. rate and rate correct10n factor fer 100 m s Rate constants and correction ractors C WLI==. 00 vv:.:!6l 0UO.U( 1: f.) ::: t H ... u 0 {) I'J l.l 0 c l j ;.: t j 6 c: .:t l l l .... 0 : :; l N Cl ;; L ') A i... U E. !:; cas1 and a r e the rluxes IJ n c-a r r e c t.. e 1 j t l J r .L n .. r FJ r t. ;-:.' i ;::. t:? r--:-., u L ::; l '" :.:: / 0 () v Ll 0 S l iW,-=!J L lNUH !LlNDH [! t e r il1 i r e ;...Jill c h c a r L1 on 1 = :J t. o ;:. e c 'J r v 2 1 s t e 1 n ::l us E j

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c 1 0 c ACL.:l:Y I J CURVE:: ( 1 > FOkMA--1 ( 1A 1) ljiJ TU 10 LlNUH "dot 1mPl1es the t1me der1vat1ve Th1; sectton calculates tne t l u;:er:; U ::: l J U iJ U 0l.i v I \ t L: -t- 0 0 C () 0 :i U L: :t ( i:.J Ll H I.J 1 1 b + i-W t_; H ) I f V==!-y;c::r.L-l

PAGE 260

c c c ('' c c c 2llll lh1s sect1on :;e:=--a>ates :-,n ;,;;-;.:; ir'!:.o that are t'unct1ons ot t a t't: an:, t11o=.e ; ,ct I :t: f '. l, 11 > 1 Calculate the correct1on factor o rt :; t a ,.j s t a t 1 Y l O = Y( 1? J.()J ... 1 16=161-.t CalctJ.tate based the emP1r1cal S reenhouse ra1at1on r ( 1 6 > ::: o o u J u .f. u i: x ; .. 1 -' 7 vi. <; z .. .: : ) u r.: 1 i. l .. :;. i : > u v-o J' ( ( :L y ,5 ) ::: ( tY:!( :t' :t: l 1 H ,.; M :J ... \ .. ;. ; \ : ; r : C; i i i-\_; t t.: l .... a 1 c 'J 1 t e t .. ii e v :.:o .:. ;::: .::. :-, c -s .;':! :.:. t. r "'. ; .. :: ;-..::; rt g i-? .,.. at. :.:. U I l '; -= L : l: )!; : ( l v 6 ) .: ... .: r ( 1 1 J. J -Y t 1 . ) i ..;. f:: { j =v. :::Ol'iJ u:.; !. :::. ) = o v o <; c v r.: o lvr=3 0 u 1 6 u .c "' 1 y i ; L :r;LL f 1 :' ;(UU i ;-< 1 t ::.. ;., ) UU lU LIU l l!:i 1-==1 ,.:.: .1. :: I ( U U ; t\ ( i ) Lj i 'j v 0 U !j 0 ) i \ i. ':. i t-: ;_! 1_; i i; .; i ) 1. (UN I

PAGE 261

c ')'")t:" -,;... ..J J2=J1 Calculate M tCal bY charse b3lance P r1nt the 1NA Mt= A;lN l V AL,LK6') 2 f"r.<::,;,:;) .;Ytlr l ) 1 1 '" 1 7 16.i 250 I F ( 1!::: 1-\ l:. I] :.:.:: ) 1 H 1::: >X ' M .:. j 6 *' UtU11:\U ::. :u :...;Ui'l : c.r:Gt 1 lll:.KA rlUNS" J: f ( 11::. x 1::: 4 j r i 11:. :l<: 1 i.5 H i:.t : u r : c: F.: 1 ti T U E N U 245


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