Phanerozoic atmospheric CO change: evaluating geochemical 2 and

Ž .Earth-Science Reviews 54 2001 349–392www.elsevier.comrlocaterearscirev

Phanerozoic atmospheric CO change: evaluating geochemical2

and paleobiological approaches

Dana L. Royer a,), Robert A. Berner a,1, David J. Beerling b,2

a Kline Geology Laboratory, Yale UniÕersity, P.O. Box 208109, New HaÕen, CT 06520-8109, USAb Department of Animal and Plant Sciences, UniÕersity of Sheffield, Sheffield S10 2TN, UK

Accepted 8 November 2000

Abstract

The theory and use of geochemical modeling of the long-term carbon cycle and four paleo-PCO proxies are reviewed2

and discussed in order to discern the best applications for each method. Geochemical models provide PCO predictions for2

the entire Phanerozoic, but most existing models present 5–10 m.y. means, and so often do not resolve short-termexcursions. Error estimates based on sensitivity analyses range from "75–200 ppmV for the Tertiary to as much as "3000ppmV during the early Paleozoic.

The d13C of pedogenic carbonates provide the best proxy-based PCO estimates for the pre-Tertiary, with error estimates2

ranging from "500–1000 ppmV. Pre-Devonian estimates should be treated cautiously. Error estimates for TertiaryŽ .reconstructions via this proxy are higher than other proxies and models "400–500 ppmV , and should not be solely relied

upon. We also show the importance of measuring the d13C of coexisting organic matter instead of inferring its value from

marine carbonates.13 Ž 3 4The d C of the organic remains of phytoplankton from sediment cores provide high temporal resolution up to 10 –10

. Ž .year , high precision "25–100 ppmV for the Tertiary to "150–200 ppmV for the Cretaceous PCO estimates that can be2

near continuous for most of the Tertiary. Its high temporal resolution and availability of continuous sequences isadvantageous for studies aiming to discern short-term excursions. This method, however, must correct for changes in growth

Ž .rate and oxygen level. At elevated PCO ;750–1250 ppmV , this proxy loses its sensitivity and is not useful.2Ž 2 .The stomatal density and stomatal index of land plants also provide high temporal resolution -10 year , high

Ž .precision "10–40 ppmV for the Tertiary and possibly Cretaceous PCO estimates, and so also is ideal for discerning2Žshort-term excursions. Unfortunately, this proxy also loses sensitivity at some level of PCO above 350 ppmV which,2

.currently, is largely undetermined .Our analysis of the recently developed d

11B technique shows that it currently is not yet well constrained. Mostimportantly, it requires the assumption that the boron isotopic composition of the ocean remains nearly constant through

) Corresponding author. Fax: q1-203-432-3134.Ž . Ž .E-mail addresses: [email protected] D.L. Royer , [email protected] R.A. Berner , [email protected]

Ž .D.J. Beerling .1 Fax: q1-203-432-3134.2 Fax: q44-0114-222-0002.

0012-8252r01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved.Ž .PII: S0012-8252 00 00042-8

( )D.L. Royer et al.rEarth-Science ReÕiews 54 2001 349–392350

time. In addition, it assumes that there are no biological or temperature effects and that diagenetic alteration of the boronisotopic composition does not occur.

A fifth CO proxy, based on the redox chemistry of marine cerium, has several fundamental flaws and is not discussed in2

detail here. q 2001 Elsevier Science B.V. All rights reserved.

Keywords: carbon dioxide; paleoatmosphere; paleoclimatology; indicators

1. Introduction

During the last decade, numerous methods forevaluating past concentration of atmospheric carbon

Ž .dioxide PCO have been developed andror re-2

fined. The most reliable method has been the deter-

mination of the composition of air trapped in glacialŽ .ice e.g., Friedli et al., 1986; Petit et al., 1999 .

However, this method is only useful for the past 400ka because of the absence of ice older than this.Thus, other methods have been applied to the oldergeologic record. Quantifying paleo-CO is vital for2

Nomenclature:

Symbols commonly used in text)C PCOa 2) 3Ž .C soil CO mol cms 2

C diunsaturated long-chained alkenones37:2) 2 y1Ž .D diffusion coefficient for soil CO cm ss 2

p rp ratio of internal:ambient COi a 2

S CO contributed by biological respiration2Ž .z depth in a soil profile cm

Ž .z characteristic CO production depth cm2Ž .a and ´ fractionation factor for diffusion during carbon fixation ‰diff diff

Ž .a and ´ kinetic fractionation factor for carbon fixation ‰f fŽ .a and ´ combined fractionation for carbon fixation ‰P P

13 Ž .d d C of the atmosphere ‰a13 Ž .d d C of pedogenic carbonate ‰cc13 Ž .d d C of CO at the site of carbon fixation ‰i 213 Ž .d d C of marine carbonate ‰occ13 Ž .d d C of organic matter ‰om13 Ž .d d C of photosynthate ‰p13 Ž .d d C of soil CO ‰s 213 Ž .d d C of soil-respired CO ‰f 211 Ž .d d B of total dissolved B ‰ÝB

´ free air porosity in soil´ ambient atmospheric partial pressure of water vapora

´ intercellular partial pressure of water vapori) y1 y3Ž .f CO production rate mol s cms 2

y1Ž .m growth rate dr tortuosity

( )D.L. Royer et al.rEarth-Science ReÕiews 54 2001 349–392 351

understanding climate dynamics, most notably itsŽeffect on global temperature e.g., Sloan and Rea,.1995; Kothavala et al., 1999 through the so-called

‘greenhouse effect’. PCO affects many other as-2

pects of the biosphere including particularly thephysiology, productivity and distribution of terres-trial vegetation. This in turn influences our interpre-

Ž .tation of the plant fossil record Beerling, 1998b andexerts an important impact on the feedback betweenvegetation and climate by changing the exchange ofenergy and water vapor between the land surface and

Ž .the overlying atmosphere e.g., Bounoua et al., 1999 .Quantifying the PCO of the ancient atmosphere,2

therefore, provides a firmer basis for assessing thelinkages between PCO and the biosphere that are2

urgently required for understanding the geologic pastŽ .Beerling, 2000 .

Here, we critically consider the underlying theory,practice, and applicability of geochemical modeling

Ž .of the long-term multimillion year carbon cycleand four paleo-PCO proxies. Several of the proxies2

were developed for and first applied to the Quater-nary, but their application to the pre-Quaternaryrecord will be emphasized here. The four proxies arethe d

13C of phytoplankton, the d13C of pedogenic

Ž .carbonates including the goethite method , stomataldensity and stomatal index, and the d

11 B of marinecalcium carbonate. In considering the applicability ofthe various approaches to the geologic record, theirassociated temporal resolutions and precision ofPCO estimates will be emphasized.2

2. Geochemical modeling of the long-term carboncycle

The level of atmospheric CO over geologic time2

can be estimated by constructing mass balance ex-pressions for all the processes that bring about inputsand outputs of CO to and from the atmosphere. This2

is a daunting task at any timescale. The best one cando is to construct theoretical models and attempt todevise rates and rate laws for processes involved inthe carbon cycle and how these rates may havechanged over time. Since this review is concernedwith pre-Quaternary PCO , only models that treat2

CO changes over millions of years will be dis-2

cussed. The carbon cycle on a multimillion year

basis is dominated by the exchange of carbon be-tween rocks and the surficial reservoir consisting ofthe atmosphereqbiosphereqoceansqsoils, and theprocesses involved in the long-term cycle are differ-ent from those that are involved in the short-termcycle, which considers only the exchange of carbon

Ž .within the surficial reservoir see Berner, 1999 .Because the amount of CO in the atmosphere is2

exceedingly small compared to the carbon fluxesinto and out of it, it is very difficult to calculatechanges in PCO due to imbalances between these2

Žfluxes over millions of years Berner and Caldeira,.1997 . Calculations of PCO from imbalances via2

Žtime-dependent modeling have been made Berner et.al., 1983; Lasaga et al., 1985 , but they require

treatment of fluxes of additional elements such asCa, Mg, and S, as well as fluxes of carbon betweenthe ocean and atmosphere as well as between rocksand the surficial reservoir. Because of their complex-ity, these models will not be covered here. Instead,simpler models dealing only with carbon, principally

Žthe GEOCARB and similar models Budyko et al.,1987; Berner, 1991, 1994; Caldeira and Kasting,1992; Francois and Walker, 1992; Kump and Arthur,1997; Tajika, 1998; Berner and Kothavala, 2001;

.Wallman, 2001 , will be discussed. Several othermodeling approaches to the long-term carbon cyclehave been made, but they do not actually calculateCO concentrations and will not be discussed here2ŽWalker et al., 1981; Caldeira, 1992; Raymo andRuddiman, 1992; Godderis and Francois, 1995, 1996;Derry and France-Lanord, 1996; France-Lanord andDerry, 1997; Gibbs et al., 1997, 1999; Kump andArthur, 1999; McCauley and DePaolo, 1997; Raymo,

.1997; Francois and Godderis, 1998 .The GEOCARB model considers the input of

CO to the atmosphere from the thermal breakdown2

of carbon in rocks resulting in volcanic, metamor-phic, and diagenetic degassing. Additional CO in-2

put comes from the weathering of organic matter inrocks exposed on the continents. Carbon dioxide isremoved from the atmosphere by the weathering ofCa–Mg silicate and carbonate minerals to form dis-solved bicarbonate in groundwater, followed bytransport of the HCOy by rivers to the oceans where3

the HCOy is removed as Ca–Mg carbonates in3

bottom sediments. Thus, carbon is transferred fromthe atmosphere to carbonate rocks. In some models


Ž .e.g., Wallman, 2001 , direct weathering of Ca–Mgsilicates to carbonates on the seafloor is also consid-ered. The burial of organic matter in both marine andnon-marine sediments also removes CO fixed by2

photosynthesis from the atmosphere.Because the mass of carbon exchanging with

rocks via volcanism, weathering, etc., over millionsof years is so much larger than that present at any

Žgiven time in the surficial reservoir atmosphereq.biosphereqoceansqsoils , it can be assumed that

for each large time step in the calculation the sum offluxes from rocks to the surficial system are essen-tially equal to the sum of fluxes back to the rocks.This is what is done in GEOCARB modeling and itis this assumption of quasi-steady state that allowsthe calculation of PCO over geologic time. It repre-2

sents the reasonable idea that extremely large massesof carbon, that would otherwise result if the fluxesdid not balance, cannot be stored in any portion of

Žthe surficial reservoir for example, the continentscan accommodate just so much biomass, and excessHCOy in the oceans will eventually precipitate as3

CaCO due to excessive supersaturation—see Berner3.and Caldeira, 1997 for further discussion .

2.1. Method of calculation

Carbon cycle models treat a large variety of pro-cesses and, therefore, involve mathematical treat-ment that is far more complex than that used for theother paleo-CO proxies discussed elsewhere in the2

present review. For this reason, the entire GEO-CARB model is not presented here but only sum-marized qualitatively with a minimum of mathema-tical expressions. Further details of the modeling

Žcan be found in the original papers Berner, 1991,1994; Berner and Kothavala, 2001; variants of GEO-CARB-type modeling are presented by others refer-

.enced above, but they rest on similar reasoning . Thefundamental basis of the GEOCARB model is twocarbon mass balance equations:

F qF qF qF sF qF 1Ž .wc mc wg mg bc bg

d F qF qd F qFŽ . Ž .c wc mc g wg mg

sd F q d ya F 2Ž . Ž .bc bc bc c bg

where: F , F s rate of release of carbon to thewc wg

atmosphereqbiosphereqoceansqsoils system viaŽ .the weathering of carbonates c and organic matter

Ž .g ; F , F s rate of release of carbon to themc mg

atmosphereqbiosphereqoceansqsoils; system viathe metamorphicrvolcanicrdiagenetic breakdown of

Ž . Ž .carbonates c and organic matter g ; F , F sbc bgŽ .burial rate of carbon as carbonates c and organic

Ž . 13 Žmatter g in sediments; d , d sd C value perc g. Ž . Ž .mil for carbonates c and organic matter g under-

13 Ž .going weathering; d sd C value per mil forbc

carbonates undergoing burial in sediments; a scŽ .carbon isotope fractionation per mil between or-

ganic matter and carbonates both undergoing burialin sediments. These equations represent the quasi-steady state equivalence of the sum of CO inputs2

Žand outputs for each time step in the modeling for.GEOCARB the time step is 1 million year .

From these equations and additional algebraicŽexpressions for each of the input fluxes terms on the

.left-hand side of the equations , and how they changewith time, one can solve the two equations for eachflux F as a function of time. This requires data onthe following subjects as they affect continentalweathering: total land area and mean continental

Ž .elevation from paleogeographic maps , relative ar-Žeas of exposure of silicate vs. carbonate rocks from

.paleogeologic reconstructions , global river runoffŽ Ž .from general circulation climate models GCMs

.applied to ancient paleogeographies , land tempera-Ž .ture from GCMs , the rise of large vascular land

plants and their quantitative effect on weatheringŽ .from modern weathering studies , the effect of solarevolution on mean global temperature and river

Ž .runoff from GCMs , the effect of changes in PCO2Žon climate and river runoff atmospheric greenhouse

.effect from GCMs , and the effect of changes inPCO on the rate of growth and weathering by land2

Ž .plants from modern plant experiments .Inputs of CO to the atmosphere are parameter-2

ized in the GEOCARB model in terms of: seafloorspreading rate as a guide to global tectonic degassingŽfrom seafloor arearage relations and paleo-sea level

.data , and the rise of calcareous plankton as theyaffect the amounts of CaCO in deep sea sediments3

subjected to heating and degassing during plate sub-duction. Organic carbon and calcium carbonate burialrates in sediments are derived from the carbon iso-


topic record of carbonates being buried at each timeŽ . Ž .step and Eqs. 1 and 2 above. A summary of these

factors considered by the GEOCARB model is shownin Table 1.

The calculation of PCO in GEOCARB modeling2Ž .sensu strictu is derived by determining the rate ofweathering of Ca–Mg silicates on land to Ca–Mgcarbonates in the oceans. This is equivalent to F ybc

Ž .F from Eq. 1 . The expression for silicate weath-wc

ering is:

F t sF yFŽ .wsi bc wc

0.65s f t f t f t f t f t F 0Ž . Ž . Ž . Ž . Ž . Ž .B H R E D wsi

3Ž .Ž .where: F t s rate of Ca–Mg silicate weatheringwsi

with ultimate conversion to Ca–Mg carbonates; theŽ . Ž .value for the present is designated as F 0 ; f twsi H

seffect on weathering of global mean land tempera-Ž .ture at some past time t rpresent global mean land

Ž .temperature; f t seffect on weathering rate ofRŽ .mean continental relief at time t rmean continental

Ž .relief at present; f t sdimensionless parameterE

expressing the dependence of weathering rate on soil

Table 1ŽOutline of processes in the GEOCARB II model after Berner,

.1991, 1994

Weathering of silicates, carbonates, and organic matterŽ .1 Topographic relief as affected by mountain upliftŽ .silicates and organic matterŽ . Ž .2 Global land area carbonatesŽ .3 Global river runoff and land temperature as affected bychanges in continental area and positionŽ .4 Relative areas of land underlain by silicates vs. carbonatesŽ .5 Rise and evolution of vascular land plantsŽ .6 Enhancement of weathering flux by changes inglobal temperature and runoffŽ .a Due to evolution of the sunŽ . Ž .b Due to changes in atmospheric CO greenhouse effect2Ž .7 Enhancement of plant-mediated weathering due tofertilization by atmospheric CO2

Thermal degassing of CO from Õolcanism, diagenesis,2

and metamorphismŽ .1 Changes in global seafloor spreading rateŽ .2 Transfer of CaCO between platforms and the deep sea3

Burial of organic matter and carbonates in sedimentsŽ .1 Calculated via mass balance from sum of input fluxesŽ .2 Relative proportions derived from carbon isotopic data

Ž Ž .biological activity due to land plants f t s1 atE. Ž . Ž .present ; f t s river runoff t rriver runoff at pre-D

Ž .sent due to changes in paleogeography; f t sB

dimensionless feedback factor representing the ef-fects of CO and temperature on weathering rate.2

Ž .The value of F 0 can be estimated from mod-wsiŽ . Ž .ern river water data and values of f t , f t ,R H

Ž . Ž .0f t , and f t are obtained via the methods out-E DŽ .lined above. With these results Eq. 3 can then be

Ž . Ž .solved for f t . The parameter f t represents theB B

effects on silicate mineral weathering of changes intemperature and runoff as they are, in turn, affectedby changes in PCO and solar radiation. Also in-2

cluded is the effect of PCO on plant-mediated2Ž .weathering. The parameter f t represents negativeB

feedback against a runaway greenhouse or icehouseclimate. Derivation of the resulting complex alge-

Ž .braic expression for f t allows solution of it forBŽ .PCO once the actual value of f t has been deter-2 B

mined.

2.2. Problems with the method

A large number of assumptions go into GEO-CARB and the similar models of Caldeira and Kast-

Ž . Ž .ing 1992 and Tajika 1998 . Simple error analysisis impossible but a rough idea of error can bedetermined by sensitivity analysis. This was done in

Žthe GEOCARB modeling Berner, 1991, 1994;.Berner and Kothavala, 2001 by varying each of the

Ž . Ž .values for f t , f t , etc., from no change from theR E

present to geologically extreme maximum and mini-mum values and examining the effect on CO . For2

example, varying the effect of different groups ofland plants on chemical weathering of Ca–Mg sili-cates results in large changes in calculated CO level2Ž .Berner, 1991, 1994; Berner and Kothavala, 2001 .Varying groups of related parameters, such as theassumption of no change in tectonic degassing, nochange in paleogeography, no evolution of landplants, etc., has also been done. Such sensitivityanalysis has allowed the construction of crude errormargins for the Abest estimateB of CO concentra-2

tion over Phanerozoic time. The error margins arelarge and show that the Abest estimatesB are proba-

Ž .bly good to only a factor of about two see Fig. 13 .Another problem lies with the limits of temporal

resolution. Data are input into the GEOCARB model


Ževery 10 million years every 5 million years for.some Cenozoic isotopic data . As a result, the model

cannot delineate short-lived events such as theŽ .Permo-Triassic and Cretaceous-Tertiary K–T ex-

tinction, the late Ordovician glaciation, and the Pale-Ž . 13ocene–Eocene P–E d C excursion. The GEO-

CARB model is intended to treat only more gradualchanges over many millions of years. However, thisdoes not preclude the application of similar carboncycle mass balance modeling to shorter timescales as

Ž .has been done by Gibbs et al. 1997 for the lateOrdovician glaciation.

Even with sensitivity analysis the model calcula-tions are no better than the various assumptionsmade by the GEOCARB model. Some of the largerproblems, ranked in order of more-to-less serious,are:

1. The content of CaCO in subducting sediments3Žis virtually unknown before the Jurassic 150

.Ma .2. The estimate of paleorelief, and its effect on

weathering, is poorly known.3. Seafloor spreading rates before the Jurassic are

not represented simply by changes in sea level,as is assumed by the model.

4. River runoff and land temperature calculationsare based on GCM calculations for flat conti-nents. Recalculation based on realistic topogra-phy is needed.

5. The effect of large shifts in the proportions ofbasalt vs. granite weathering has not been eval-uated.

6. Little is known of how changes from gym-nosperms to angiosperms affected the rate ofplant-mediated weathering.

7. Global degassing may not scale linearly withseafloor spreading rate as assumed.

Ž8. Other factors have been ignored midplate su-perplume degassing, seafloor basalt weather-

.ing, etc. .

2.3. Summary

The carbon cycle modeling method has manyinherent problems, but it at least considers and dis-cusses the processes that actually bring about changesin atmospheric CO over geologic time. It is always2

amenable to modification and improvement. Themethod is best evaluated by its agreement or lack ofagreement with the other methods. As an example,there is surprisingly good agreement, within errorranges for each method, between the PCO values2

calculated via GEOCARB modeling and those de-Žrived from the study of carbonate paleosols see Fig.

.14 .

3. d13C of phytoplankton

The carbon isotopic composition of biomass is afunction of the carbon source, the carbon assimila-tion pathway, and the biosynthesis and metabolismof the assimilated organic carbon. In sedimentaryorganic matter, diagenetic processes may also beimportant. In the case of autotrophs, the carbonassimilation pathway often strongly alters the carbonisotopic signature relative to the carbon source. Forexample, the equilibrium and kinetic isotope effectsassociated with photosynthesis consistently fraction-ate strongly against 13C. One factor that affects thesefractionations in phytoplankton is the concentration

Žw x. Žof CO dissolved in water CO Degens et al.,2 2Žaq..1968; McCabe, 1985 . This relationship is often

inverted and applied to the geologic past to estimatepaleoatmospheric CO , ranging from the late Trias-2

Žsic to Quaternary Popp et al., 1989; Jasper andHayes, 1990; Freeman and Hayes, 1992; Pagani et

.al., 1999a,b .

3.1. Photosynthetic fractionation of 13C

Two processes fractionate the carbon pool duringphotosynthesis: the equilibrium isotope effect of CO2

diffusion at the boundary layer of the photosynthe-sizer, and the kinetic isotope effect of CO fixation.2

The difference in diffusivity for two isotopes in agiven gas is proportional to the square root of their

Ž .reduced masses Mason and Marrero, 1970 ; in air,13 12 ŽCO is 4.4‰ less diffusive than CO Craig,2 2

. Ž1953 , and for water the difference is 0.7‰ O’Leary,

.1984 . This fractionation factor can be expressed asthe following:

1000qdaa s 4Ž .diff 1000qd i


where a s fractionation due to diffusion, d sdiff a

d13C of the atmosphere, and d sd

13C at the site ofi

fixation. The kinetic effect associated with carbonŽfixation is usually driven by rubisco ribulose-1,5-bi-

.phosphate carboxylase oxygenase , the enzyme thatŽcatalyzes the reaction between RuBP ribulose-1,5-

. Žbiphosphate and CO to form PGA 3-phosphog-2

.lyceric acid , a 3-carbon acid. In vitro, there is a13 Ž29‰ fractionation against C at 258C Roeske and

.O’Leary, 1985 . In vivo, however, the value forŽvascular plants is closer to 27‰ Evans et al., 1986;

.Farquhar et al., 1982 and 25‰ for phytoplanktonŽLaws et al., 1995; Bidigare et al., 1997; Popp et al.,

.1998; Hayes et al., 1999 . These discrepancies arelikely due to both a drop in CO from the intercellu-2

lar spaces to the site of fixation and a f10% oftotal carbon fixation via PEP carboxylase, an enzyme

13 Žthat only mildly fractionates against C Farquhar.and Richards, 1984 . The kinetic fractionation factor

can be expressed as the following:

1000qd ia s 5Ž .f 1000qdp

where a skinetic fractionation associated with car-f

bon fixation, and d sd13C of the photosynthate.p

Although the fractionations associated with photo-synthesis are highly invariant, for a given d , d cana p

vary by as much as 15‰, particularly for photosyn-Žthesizers in stressed environments e.g., water stress

. Ž .in land plants, nutrient stress . Farquhar et al. 1982proposed that this variation is principally a function

Ž .of the ratio of internal CO to ambient CO p rp .2 2 i a

In essence, the d13C of inorganic carbon within

photosynthesizers follows a Rayleigh distillation pro-cess, with p rp controlling how closed the systemi a

is. This relationship can be expressed as the follow-Ž .ing after Farquhar et al., 1982; Popp et al., 1989 :

a sa q a ya p rp 6Ž . Ž .P diff f diff i a

where a s fractionation factor integrating the twoPŽ Ž .isotopic fractionations described above Eqs. 4 and

Ž ..5 . This can be recast in terms of ´ values, whereŽ . 3´' ay1 =10 :

´ '´ q ´ y´ p rp . 7Ž . Ž .P diff f diff i a

For phytoplankton, the following values for ´diffŽ .and ´ can be substituted see above :f

´ '0.7q24.3 p rp . 8Ž .P i a

ŽIn most vascular plants, stomata pores throughwhich plants exchange gases and other constituents

.with the atmosphere help regulate CO within their2

mesophyll. If the CO external to a leaf rises or2

carbon assimilation rates drop, stomata-bearing plantsrespond by reducing their stomatal pore area, andvice-versa, so that p rp usually remains at approxi-i a

Žmately 0.7 Polley et al., 1993; Ehleringer and Cer-ling, 1995; Beerling, 1996; Bettarini et al., 1997;

.Arens et al., 2000 , particularly for unstressed plants.Phytoplanktons lack stomata and consequently haveless control over p rp . Furthermore, the diffusion ofi a

CO in water is about 104 times slower than in air,2

suggesting again less internal control over p rp .i a

One might, therefore, expect a stronger correlation inw xphytoplankton between CO and ´ .2Žaq. P

[ ]3.2. Correlation between CO and ´2(aq) P

Ž .McCabe 1985 experimentally quantified the re-w xlationship between CO and ´ using mixed2Žaq. P

algal populations from several New Zealand lakes:

´ s 17.0"2.2 log CO y3.4Ž .P 2Žaq .

2F CO F74mM 9Ž .2Žaq .

where the uncertainty represents the 95‰ confidenceŽ .interval. Rau et al. 1989, 1991b measured d andp

w xcalculated CO for the South AtlanticrWeddell2Žaq.Sea and the Drake Passage, and found the followingrelationships:

S. Atlantic d sy0.8 CO y12.6Ž . a 2Žaq .

8- CO -24mM 10Ž .2Žaq .

Drake Passage d sy0.90 CO y9.40Ž . a 2Žaq .

15- CO -23mM. 11Ž .2Žaq .

Ž .Jasper and Hayes 1990 established a similarrelationship using reconstructed ´ values from aP

late Quaternary hemipelagic sediment core and cor-


w x Ž .Fig. 1. Reported values for the relationship between ´ and CO using various techniques and settings oceanic and lacustrine .P 2Žaq.Ž Ž . Ž . Ž ..Equations given in text Eqs. 9 , 12 – 17 .

w xresponding CO values calculated from the Vos-2Žaq.tok ice core:

´ s32.9log CO y14.3P 2Žaq .

5- CO -8mM. 12Ž .2Žaq .

Ž .Hollander and McKenzie 1991 also generated anw xestimate of this relationship, calculating CO2Žaq.

and ´ over an annual cycle in Lake Greifen,P

Switzerland:

´ s11.64log CO y3.56P 2Žaq .

10- CO -90mM. 13Ž .2Žaq .

Ž .Freeman and Hayes 1992 compiled GEOSECSdata from several ocean basins, and found the fol-

w xlowing relationship between calculated CO and2Žaq.´ :P

´ s12.03log CO q1.19P 2Žaq .

8- CO -25mM. 14Ž .2Žaq .

Ž .Hinga et al. 1994 experimentally grew the di-atom Skeletonema costatum at three temperatures.After accounting for possible pH effects, the follow-ing relationships were observed:

98C ´ s11.21log CO q8.99Ž . P 2Žaq .

10- CO -50mM 15Ž .2Žaq .

158C ´ s13.06log CO q8.58Ž . P 2Žaq .

5- CO -125mM 16Ž .2Žaq .

258C ´ s9.09log CO q1.89Ž . P 2Žaq .

17- CO -115mM. 17Ž .2Žaq .

The results of the five studies solving for ´ areP

shown in Fig. 1. Significant variations among theestimates exist. Using Henry’s law to convertw x ŽCO to PCO after Freeman and Hayes, 1992;2Žaq. 2

.see Section 3.5 , Miocene ´ values of 15.8‰P


Ž .Freeman and Hayes, 1992 yield a PCO estimate2Ž .of 400 ppmV using the regression of McCabe 1985

but 1400 ppmV using Hollander and McKenzieŽ . Ž1991 ; early Cretaceous values of 21.2‰ Freeman

.and Hayes, 1992 yield an estimate of 1000 ppmVŽ .using McCabe 1985 but 4900 ppmV using Hollan-

Ž .der and McKenzie 1991 . Beyond the differencesamong these logarithmic relationships, it is not clearbased on the above discussion whether the relation-

w xship between CO and ´ should be logarithmic2Žaq. PŽor linear Rau et al., 1991a; Freeman and Hayes,

. Ž1992 . This will be discussed in detail below Sec-.tion 3.4 .

3.3. Determining paleo-´P

Ž Ž ..As defined above Eq. 7 , ´ represents theP

fractionation of 13C due to photosynthesis. For mostmodern phytoplankton, ´ ranges between 10‰ andP

20‰. Calculating this value is not straightforward,particularly in fossil material where p rp is un-i a

known. Instead, modern relationships between whatŽ .can be measured e.g., carbonates, organic carbon

and ´ are used to infer paleo-´ . Fig. 2 shows theP P

modern isotopic relationships between ´ and car-P

bonates and organic carbon.The use of bulk organic carbon to estimate ´ P

ŽArthur et al., 1985; Dean et al., 1986; Kump et al.,.1999 likely leads to erroneous estimates of paleo-Ž .CO Hayes et al., 1989b; Pagani et al., 2000 due2

both to the input of terrigenous organic matter andnon-primary marine photosynthate. As discussed

Ž .above Section 3.1 , terrestrial plants are betterequipped to regulate p rp , and as a consequencei a

their carbon isotopic variability over geologic timeŽ .where large PCO fluctuations likely occurred is2

much smaller than that for marine organic carbonŽDean et al., 1986; but see Bocherens et al., 1993;

.Jones, 1994 . Likewise, carbon isotopic trends innon-photosynthetic organic material will also not

likely follow the phytoplankton trend because theircarbon is, at best, several steps removed from pri-mary marine photosynthate.

In response to this limitation, specific biomarkersfor photosynthesis have been identified and mea-

Žsured in lieu of bulk organic matter Hayes et al.,.1987, 1989b; Jasper and Hayes, 1990 . Geopor-

phyrins, derived from the aromatic nucleus ofŽ .chlorophyll Ekstrom et al., 1983; Hayes, 1993 , are

one such biomarker used in paleoatmospheric CO2Žreconstructions Popp et al., 1989; Freeman and

.Hayes, 1992 . While terrestrial plants are a potentialsource of geoporphyrins, the presence of geopor-phyrins in marine settings is probably negligibleŽ .Hayes et al., 1989b . The appropriate isotopic path-ways are shown in Fig. 2. In modern plants, geopor-

Ž .phyrin precursors e.g., chlorophyllide are enriched13 Žin C relative to bulk biomass by f0.5‰ Hayes et

.al., 1987 . Based on theoretical considerations, theconversion of this precursor to geoporphyrins proba-bly does not involve any isotopic fractionation. If a

Žfractionation does exist e.g., preferential decomposi-12 .tion of C it may, for example, be expected to be

Žlarge in highly oxygenated environments Hayes et.al., 1989b . The effects of thermal diagenesis have

also been shown to be negligible, and can always beverified by comparing geoporphyrin d

13C valueswith those of another class of compounds, for exam-

Ž .ple geolipids Hayes et al., 1989a .Ž .Diunsaturated long-chained alkenones C are37:2

Žalso used as a biomarker Jasper and Hayes, 1990;.Jasper et al., 1994; Pagani et al., 1999a,b , but are

preserved in sediments back only to the CenomanianŽ . Ž .ca. 95 Ma Farrimond et al., 1986 , and are scarcein pre-Neogene sediments. Unlike geoporphyrins,C alkenones are specific to certain haptophytic37:2

Ž . Ž .algae Prymnesiophyceae Conte et al., 1994 , en-suring that their isotopic signatures are not diluted byterrestrial contaminants. Thus, when using these

w xalkenones, one can eliminate the CO –´ rela-2Žaq. P

13 Ž .Fig. 2. Isotopic relationships between preserved carbonates and organic matter. Values are for d C. Modified after Hayes et al. 1989b .


tionships not based solely on these haptophytic algaeŽ .see Fig. 1 . In the modern open-ocean, C37:2

alkenones are only synthesized by Emiliania huxleyiŽand its relative Gephyrocapsa oceanica Marlowe et

.al., 1990; Conte et al., 1994 , both of which are mostcommon at mid-latitudes. Laboratory analyses findC alkenones f4‰ lighter than bulk haptophytic37:2

Žbiomass Jasper and Hayes, 1990; Bidigare et al.,.1997; Popp et al., 1998 . In addition, the unsatura-

Žw x w x.tion ratios of C alkenones C r C qC37 37:2 37:2 37:3Žare correlated with temperature Brassell et al., 1986;

.Prahl and Wakeham, 1987 , and have been useful foralkenone-based paleo-CO work in the Quaternary2Ž . ŽJasper et al., 1994 , but not the Miocene Pagani et

.al., 1999a .As shown in Fig. 2, at least two fractionations

exist between CO and preserved carbonates.2Žaq.CO is enriched in d

13C when converted to HCOy2Žaq. 3

and again further to calcite. A common value as-Ž .signed to these combined fractionations at 258C is

Ž .10.8‰ e.g., Popp et al., 1989; see Fig. 2 . Thisvalue can vary among species, for example, 9.3‰

Žfor Globigerinoides ruber at 248C Jasper and Hayes,.1990 . The fractionations are also temperature de-

pendent, and recent paleo-CO studies have used2

shallow water d18 O reconstructed temperatures to

Žsolve for these fractionation factors Freeman and.Hayes, 1992; Pagani et al., 1999a,b . One quantifica-

Žtion of this dependency is after Romanek et al.,.1992; Mook et al., 1974, respectively :

´ yCO s11.98y0.12T 8C 18Ž . Ž .calcite 2Žg .

´ yCO s0.19y373rT K 19Ž . Ž .CO 2Žg .2Žaq .

so that at 258C, ´s10.0‰.Diagenetic processes such as reprecipitation and

differential dissolution can also affect isotopic com-positions. The presence of recognizable nannofossilsand frequency of bioturbation and incomplete ce-mentation are typically used to gauge the severity of

Ž .diagenesis Hayes et al., 1989b; Pagani et al., 1999a .Comparison of SrrCa ratios with that in unaltered

Žcontemporaneous calcite can also be used Hayes et.al., 1989b since SrrCa ratios are lower in non-bio-

Žgenic calcite than in biogenic calcite Baker et al.,.1982 .

Given the above guidelines, ´ can be calculatedP

as follows:

d q1000d´ ' y1 =1000fd yd 20Ž .P d p

d q1000p

where d sd13C of CO , and d sd

13C of thed 2Žaq. p

bulk primary photosynthate. Assuming no carbonatediagenesis, d can be calculated from the organicd

matter’s associated calcite. Assuming no secondaryprocessing of the organic biomarker, d can bep

calculated from the biomarker. For geoporphyrins,the corresponding fractionation factor is f0.5%,and for C alkenones, f4‰. Thus, using the37:2

alkenone biomarker for sediments with a shallowwater paleotemperature of 258C and the fractionation

Ž . Ž .factors in Eqs. 18 and 19 , ´ can be estimatedP

by:

d q990d´ s y1 =1000. 21Ž .p

d q996p

3.4. Other confounding factors in determining ´P

Ž Ž ..As discussed above see Eq. 7 , ´ is a functionPw xof p rp , where p represents CO just outsidei a a 2Žaq.

the boundary layer of the cell. This CO need not2

equal the global mean concentration, e.g., in areas ofŽupwelling or in stagnant, stratified waters Popp et

al., 1989; Freeman and Hayes, 1992; Goericke et al.,. w x1994 . The global mean CO is required to2Žaq.

Ž .accurately estimate PCO see Section 3.5 . One2

approach to minimize this potential bias is samplingŽsites associated with low productivity Pagani et al.,

.1999a,b .Different species may fractionate carbon differ-

Ž .ently during photosynthesis. Hinga et al. 1994 foundŽ´ values 8–10‰ lighter in E. huxleyi a hapto-P

. Ž .phytic alga than in S. costatum a diatom underidentical conditions. This problem can be largelyremoved by using C alkenones, since their pro-37:2

duction is restricted to one taxon.w xAt low CO , some types of phytoplankton2Žaq.

y Žappear to actively transport HCO Hinga et al.,3

1994; Laws et al., 1995, 1997; Popp et al., 1998; but. Ž .see Bidigare et al., 1997 . Laws et al. 1995 con-

cluded that the diatom Phaeodactylum tricornutum


y w xprobably actively transports HCO when CO3 2Žaq.Ž .-10 mM. Bidigare et al. 1997 and Laws et al.

Ž .1997 report a similar threshold for other species. Ifthe conversion from bicarbonate to carbon dioxideoccurs intracellularly, the subsequent enhanced

Ž .growth rate see Fig. 3 will likely offset the heavyy Ž .carbon supplied by the HCO Laws et al., 1995 . If3

the conversion occurs extracellularly, the resultingw xelevated growth rate is still expected but the CO2Žaq.

supplied by the bicarbonate will probably be similarŽto the bulk CO . This, in turn, may affect ´ Laws2 P

. yet al., 1995 . This extracellular conversion of HCO3

to CO is probably the most common active2Žaq.Ž .pathway Laws et al., 1997 . Additionally, many

types of phytoplankton fix HCOy with PEP carbox-3Žylase, which lead to lower ´ values see SectionP

.3.1 . Most importantly, this rate of fixation mayw xdepend on CO , and thus covary with PCO2Žaq. 2

Ž .Hinga et al., 1994; Reinfelder et al., 2000 .

Ž .Growth rate Fry and Wainwright, 1991 and cellŽ .geometry Popp et al., 1998 can also influence ´ .P

If p is purely supplied by diffusion in phytoplank-iŽ .ton i.e., no active transport , the growth rate m

Ž y1 .d is proportional to the difference between pa

and p :i

msk p yk p . 22Ž .1 a 2 i

Ž .If this is solved for p and substituted into Eq. 7 ,i

the following relationship is found where growth rateŽis negatively correlated with ´ Rau et al., 1992;P

Francois et al., 1993; Goericke et al., 1994; Laws etal., 1995; Bidigare et al., 1997, 1999b; but see Hinga

.et al., 1994; Popp et al., 1998, 1999 :

´ s´ q ´ y´ k ymrp rk . 23Ž . Ž . Ž .P diff f diff 1 a 2

This equation provides a mechanism for the loga-rithmic behavior previously observed when ´ wasP

w x Ž y1 .Fig. 3. Relationship between ´ and mr CO , where msgrowth rate d . Data include mean for the modern ocean and experimentalP 2Žaq.Ž 2 .results under light:dark cycles of 24:0 and 12:12 h. Regression equation for 24:0-h cycle: ysy0.015xq0.371 ns5; r s0.97 . Data

Ž .from Laws et al. 1995 .


Žw x. Ž .plotted against p CO Fig. 1 . In contrast,a 2Žaq.a linear relationship exists between ´ and mrPw x Ž .CO Fig. 3 . Since experimental ´ values are2Žaq. P

w x Žconsistently f25‰ when mr CO s0 Laws et2Žaq.al., 1995; Bidigare et al., 1997; Popp et al., 1998; see

.Fig. 3 , k and k must be proportional to each1 2

other. The slopes, however, need not be equal forŽ .different species. Popp et al. 1998 calculated, how-

ever, that a 20-fold difference in slope among fourspecies when experimentally plotting ´ vs.P

w x Žmr CO was removed when cell geometry i.e.,2Žaq..cellular carbon content to surface area ratio was

Ž .considered. Popp et al. 1999 observed similar be-havior in the modern Southern Ocean. Thus, k rk1 2

may largely be a function of the carbon content tocell surface area ratio.

Fossil studies are generally limited in quantifyingŽgrowth rate and cell geometry. Bidigare et al. 1997,

. Ž 2 .1999a observed a striking correlation r s0.82 inw 3yxmodern oceans between PO and ´ , and as-4 P

cribed the covariation to growth rates. Assuming a´ maximum of 25‰, this relationship is as follows:P

3y25y´ CO s158 PO q49. 24Ž . Ž .P 2Žaq . 4

Ž .Pagani et al. 1999a,b assumed k sk , solved1 2Ž . Ž .Eq. 23 for m, then substituted Eq. 24 for m in Eq.

Ž .23 . Fossil sites were then carefully selected tocorrespond with stable, low productivity areas in the

w 3yxpresent-day so that modern PO values for these4

areas could be applied to the fossil sites. Given thesew 3yxPO estimates, ´ could then be calculated. Bidi-4 P

Ž .gare et al. 1997 suggested CdrCa ratios might alsow 3yxbe useful as a PO proxy. Cell geometry is more4

difficult to quantify in fossil studies, where in mod-ern plankton can be approximated by their volume to

Ž .surface area ratio Popp et al., 1998 . This variablemay be insignificant in C alkenone studies, how-37:2

ever, since they are restricted to a few species that inmodern oceans show little volume to surface area

Ž .variation Pagani et al., 1999a . Thus, assuming k1

sk in these studies may not introduce large errors.2

In addition, ´ in alkenone-producing species ap-PŽ .pears insensitive to growth rate Popp et al., 1998 .

Ž .Hinga et al. 1994 demonstrated that a shift inpH from 7.9 to 8.3 induced a ´ change of 10‰.P

Little other evidence concerning this factor exists.Although virtually impossible to observe or calcu-

late, changes in cell membrane diffusivity could alsoŽ .affect ´ Goericke et al., 1994 . Finally, the diatomP

P. tricornutum was recently found to discriminate13 Ž .more strongly against C 1.4‰ in a 32.5% vs.

Ž .22% O atmosphere Berner et al., 2000 . The effect2

is ascribed to carbon recycling via photorespiration,which is partially a function of the O to CO ratio.2 2

This ratio was probably higher than today during thelate Paleozoic and lower during, for example, the

Žearly and mid-Mesozoic Berner and Canfield, 1989;.Berner et al., 2000 . Since photorespiration in mod-

Ž .ern phytoplankton is low Burns and Beardall, 1987 ,this effect may only be important for late Paleozoicreconstructions.

[ ]3.5. ConÕerting CO to PCO2(aq) 2

w xOnce CO is calculated, it must be converted2Žaq.to PCO . According to Henry’s law, this relationship2

is a partial function of temperature. For example, thew xincrease in CO solubility with decreasing tem-2Žaq.

w xperature explains the anomalously high CO and2Žaq.Žcorresponding ´ values at high latitudes Rau etP

al., 1989, 1991b; Popp et al., 1999; Andrusevich et.al., 2000 . Salinity also influences this relationship,

Žbut is generally disregarded in paleostudies e.g.,.Pagani et al., 1999a,b . One also assumes equilib-

Žrium between CO and atmospheric CO e.g.,2Žaq. 2.Freeman and Hayes, 1992; Pagani et al., 1999a,b .

Large sections of the modern ocean are up to "50ŽppmV out of equilibrium with the atmosphere Tans

.et al., 1990 , and slightly larger values have beenŽ .calculated for the Quaternary Jasper et al., 1994 ,

making this a dangerous assumption. Pagani et al.Ž .1999a,b selected low productivity sites, which typi-cally are closest to equilibrium with respect to CO .2

3.6. Summary

Several studies have estimated paleoatmosphericCO from the d

13C of marine phytoplankton, both2Žfor the Quaternary Jasper and Hayes, 1990; Rau et

.al., 1991a; Jasper et al., 1994 and pre-QuaternaryŽ .Freeman and Hayes, 1992; Pagani et al., 1999a,b .

Ž .Interestingly, White et al. 1994 used an analogoustechnique for mosses, which lack foliar stomata,spanning the Holocene.


Many relationships and assumptions are requiredto estimate PCO from the d

13C of phytoplankton.2Ž .Pagani et al. 1999a propagated errors from theirw 3yx Ž .estimates of PO "0.1 mM , temperature4

Ž . Ž . Ž ."28C , salinity 35"1‰ , ´ 26"1‰ , slopefw 3yx Žand intercept of PO –m relationship 11%, repre-4

senting the 95% confidence interval in the modern. 13 Ž .dataset , and analytical error for d C "0.5‰37:213 Ž .and d C "0.2‰ , and calculated an errorcalcite

envelope for PCO of 15%. This error envelope is2

not likely to decrease substantially in future studiesw xsince the ´ – CO relationship for CP 2Žaq. 37:2

alkenones is currently the most reliable. As discussedŽ .above Section 3.4 , its reliability stems from the

narrow range of species producing the alkenones, thespecies’ narrow range of cell geometry, and their

Ž .observed insensitivity in terms of ´ to growthPŽ .rate. Pagani et al. 1999a,b also selected stable, low

productivity sites, which help minimize non-climati-w xcally driven fluctuations of CO due to processes2Žaq.

such as upwelling. Such settings also minimize varia-Žtion in growth rate and cell geometry Popp et al.,

. w x1998 . CO in regions of low productivity are2Žaq.also more likely to be in equilibrium with PCO .2

Ž .Pagani et al. 1999a,b estimated PCO from a site2Ž .ODP 588 with relatively high paleo-surface sea

Ž .temperatures 15–228C . Due to the higher concen-trations of CO in colder water, ´ in cold water2Žaq. P

Žphytoplankton is less sensitive to PCO Francois et2.al., 1993; Popp et al., 1999 , and thus warm water

sites are preferable.One drawback to the use of C alkenones is37:2

their relative scarcity in many sediments, particularlyat higher latitudes and in pre-Neogene sedimentsŽ .Marlowe et al., 1990 . For pre-Cenomanian sites,where C alkenones are unknown, another37:2

biomarker is required, which at present would de-crease the precision of PCO estimates. A general2

drawback to the use of marine phytoplankton as aPCO indicator is its decreased precision at high2

PCO , where ´ asymptotically approaches 25‰.2 p

This break in slope usually occurs between 750 andŽ .1250 ppmV CO Kump and Arthur, 1999 .2

The temporal resolution of this proxy can be quitehigh, particularly in densely sampled ocean sediment

Ž .cores e.g., Pagani et al., 1999a,b . In the case ofŽ .Pagani et al. 1999a , the average sampling density

was approximately 200 ka. The time that each sam-

ple integrated is less in most cases. This temporalŽresolution exceeds both geochemical models Sec-

.tion 2 and the method of pedogenic carbonatesŽ .Section 4 , but is generally less than the method of

Ž .stomatal parameters Section 5 . The precision ofŽindividual PCO estimates is also quite high "8–2

15% in the cases of Freeman and Hayes, 1992;.Pagani et al., 1999a,b . Again, this level of precision

exceeds that of models and pedogenic carbonates,but is generally exceeded by stomatal parameters.

4. d13C of pedogenic carbonates

4.1. The model

In regions receiving less than approximately 800Žmm annual precipitation, pedogenic carbonates i.e.,

. Žauthigenic carbonates in soils are common Royer,.1999 . In the case of CaCO , the principal source of3

calcium is wind-blown dust and dissolved Ca2q inŽ .rainwater Gile et al., 1979 . The carbonate ion is

Žtypically inherited from biological respired CO e.g.,2.organic decomposition, root respiration , not carbon-

Žate weathering or groundwater CO Cerling et al.,2.1989; Quade et al., 1989 . This is because the rate of

pedogenic carbonate formation is 102 to 103 timesŽslower than the rate of soil respiration Cerling,

.1984, 1999 . Since this biological CO flux domi-2Ž .nates hereafter referred to as soil-respired CO , soil2

CO in well-aerated soils can be modeled as a2Žstandard diffusion–production equation Baver et al.,

.1972; Kirkham and Powers, 1972; Cerling, 1984 :

EC) E2 C)

s s) )sD qf z 25Ž . Ž .s s2Et Ez

) Ž y3 .where C ssoil CO mol cm , zsdepth in thes 2Ž . )soil profile cm , and f sCO production rate as as 2

Ž y1 y3. )function of depth mol s cm . D sdiffusionsŽ 2 y1.coefficient for CO in the soil cm s , and is2

calculated as follows:

D)sD ´r 26Ž .s air

where D sdiffusion of CO in the atmosphere,air 2

which is a function of pressure and temperature,Ž .´s free air porosity in the soil 0-´F1 , and

Žrs tortuosity factor fpermeability, where 0-rF. ) Ž1 . D is assumed constant with depth Cerling,s

.1991 .


Ž ) .The CO production term f is modeled to2 sŽexponentially decay with depth Dorr and Munnich,¨ ¨

.1990 , such that:) )f z sf 0 exp yzrz 27Ž . Ž . Ž . Ž .s s

Ž .where zscharacteristic CO production depth cm2Ž .Cerling, 1991 . The model is insensitive whether

) Ž .f z exponentially decays, linearly decays, or re-s

mains constant, so long as the characteristic depthŽ . Ž .z is correct Solomon and Cerling, 1987 . z is not

Ž .highly constrained in modern soils Cerling, 1991 ;Ž .however, Dorr and Munnich 1990 report values of¨ ¨

10–20 cm for forested soils; deeper values can beŽ .expected in grasslands Cerling, 1991 .

Ž .Under steady-state conditions, Eq. 25 equalszero. Given the following boundary conditions:

) Ž . ) ) ) Ž .C 0 sC where C sPCO , and C L sks a a 2 s

where L is the depth of an impermeable boundaryŽ .e.g., groundwater table and k is a constant, the

Ž . Ž .general solution to Eq. 25 is Cerling, 1991 :

C) z sS z qC) 28Ž . Ž . Ž .s a

Ž .where S z represents the concentration of CO con-2

tributed by biological respiration, and is given as:

) 2f 0 zŽ .sS z s 1yexp yzrz . 29Ž . Ž . Ž .

)Ds

Thus, soil CO represents a mixture of atmo-2Ž .spheric and soil-respired CO . Eq. 28 can be recast2

13) Ž .in terms of the d C of C Cerling, 1984, 1991 .s

This transformation involves the assumption thatsoil-respired CO has the same isotopic composition2

as soil organic matter. The resulting expression is:

Ž .d zs

) RD Rfs a)Ž .S z qCa13 ž /ž /1qR 1qRD1 f as

s y1) )RD CR fs aPDB� 0Ž .S z 1y q13 ž /ž / ž /1qR 1qRD f as

=1000 30Ž .where d sd

13C of soil CO , D13sdiffusion coeffi-s 2 s13 Ž 2 y1.cient of CO in soil cm s , and R , R , and2 f a

R s13Cr12 C ratios of soil-respired CO , atmo-PDB 2

spheric CO , and the PDB standard, respectively.2

Note that the terms enclosed within the inner brack-

Ž . 13 12ets in Eq. 30 represent the Cr C ratio of soilŽ . Ž .CO d Cerling, 1999 .2 s

Ž . Ž .Eqs. 28 and 30 can be transformed and simpli-fied to solve for C) , the concentration of atmo-a

Ž .spheric CO Davidson, 1995; Cerling, 1999 . The2

resulting expression is:

d y1.0044d y4.4s f)C sS z 31Ž . Ž .a

d yda s

where d and d sd13C of soil-respired CO andf a 2

atmospheric CO , respectively.2

4.2. Patterns in d13C of pedogenic carbonate in

modern soil profiles

If pedogenic carbonates form in equilibrium with13 Ž .soil CO , their d C values d can be used as a2 cc

proxy for d . d measurements in modern soilss ccŽ .formed during the Holocene validate this assump-

Ž .tion Quade et al., 1989; Cerling et al., 1991a . Fig.4 shows the striking correlation between field mea-

Žsurements from one soil profile from Nevada Quade.et al., 1989 and the equilibrium-based model predic-

Ž .tion Cerling, 1984 . Fig. 4 also verifies the underly-Ž .ing assumption that d and, by extension, d iss cc

determined by the diffusion of atmospheric and soil-respired CO , with little influence from groundwa-2

ter, parent material, or kinetic or Rayleigh distillationfractionations. If this condition were not met, onewould expect heavier d values and more variationcc

Ž .at depth. Cerling et al. 1989 measured d and thecc13 Ž .d C of coexisting organic matter d in 10 mod-om

ern soils at depth, where the contribution of d undera

today’s PCO levels is minimal. d was enriched2 cc

14–16‰ relative to d , consistent with the equilib-om

rium fractionations between these two components.The sharp decrease in d at shallow soil depths iscc

typical, and represents mixing between heavy d anda

light d . Ed rEz approaches zero by 50 cm soilf s

depth in most pedogenic carbonate-producing soilsŽ .Cerling, 1984; Ekart et al., 1999 . Thus, in paleosolwork where z is not known precisely, one mustcontrol for this variability by ensuring that measuredcarbonates are at least 50 cm from the paleosurface.At times of high PCO , this asymptotic value of d2 cc

will shift to heavier values, and vice-versa for timesof low PCO .2


13 Ž .Fig. 4. Measurements of d C of pedogenic carbonate d as a function of depth from one soil profile. This soil profile developed oncc) Ž .limestone parent material. Solid line represents model prediction based on best estimates of soil temperature, ´ , r, z, f z , d , and d .s f a

Ž .Figure redrawn from Quade et al. 1989 .

( )4.3. Estimating S z

Ž .The estimation of atmospheric CO from Eq. 302

hinges on a number of relationships and associatedŽ .assumptions. The components of S z must be esti-

mated, namely soil temperature, pressure, porosityŽ . Ž .´ , tortuosity r , characteristic CO production2

)Ž . Ž Ž ..depth z , and soil CO respiration rate f 0 .2 s)The model is particularly sensitive to ´ , z, and fs

Ž .0 . For example, using a typical modern pedogenicŽ .carbonate-forming soil Cerling, 1991 with a d ofcc

y7‰, a z of 10 cm yields a PCO estimate of 25002

ppmV, but increases to 5000 ppmV for a z of 20cm. Fortunately, excursions in one or more of thesesix variables is often balanced by shifts in one or

Ž .more of the other variables Cerling, 1999 . There-fore, it is not unreasonable to combine these factors

Ž . Ž .and estimate S z directly. S z , as presented above,is the component of C) from soil respiration. Thiss

value is not well constrained in modern soils, butŽ .current data suggest values of S z at depths )50

cm for pedogenic carbonate-producing soils of3000–5000 and 5000–9000 ppmV for low and high

Žproductivity soils, respectively Brook et al., 1983;.Solomon and Cerling, 1987; Cerling, 1999 . Again,

using a typical modern soil with a d of y7‰, accŽ .S z of 3000 ppmV yields a PCO estimate of 20002

Ž .ppmV, but increases to 5500 ppmV for a S z ofŽ .9000 ppmV see Fig. 5 .

Carbonates can form at depth in waterloggedŽ .gleyed soils. Such soils can have values of S z

exceeding 25,000 ppmV, causing overestimation ofŽ .PCO Cerling, 1991 . Thus, soils with gleyed fea-2

tures should be avoided. Pedogenic carbonates alsoform in desert soils, which typically have values ofŽ . Ž .S z below 3000 ppmV Cerling, 1991 and should

also be avoided. Desert soils usually have neitherpedogenic carbonates at depths exceeding 50 cmŽ .Royer, 1999 nor well-developed leached horizons.Conversely, non-desert soils rarely have pedogeniccarbonates within the upper 20 cm of the profileŽ .Cerling, 1991 .

No pattern in the current literature emerges be-Ž .tween the S z chosen for model calculations and

the environmental context of the paleosol. Values forŽ . ŽS z range from 3000 to 5000 Ghosh et al., 1995;

. Ž .Lee, 1999 , 3000 to 7000 Mora et al., 1996 , 5000Žto 10,000 Mora et al., 1991; Cerling, 1992b; Lee

. Žand Hisada, 1999 , and 10,000 ppmV Andrews et.al., 1995 . As discussed above, pertinent values of

Ž .S z for pedogenic carbonate-forming soils are notwell constrained, but highly productive soils havevalues closer to 9000 ppmV while less productivesoils lie closer to 3000 ppmV. Given the sensitivity


Ž . Ž .Fig. 5. Sensitivity of PCO estimates to S z . The three plotted values of S z span the expected range for pedogenic carbonate-forming213 Ž . Ž . Ž .soils. Note that sensitivity increases with heavy pedogenic carbonate d C values d i.e., high PCO . Lines drawn from Eq. 31cc 2

assuming D s9.0‰, d sy6.5‰, and d sy26%.cc – s a f

of the model to this variable, more research is re-quired.

Ž .Recently, Ekart et al. 1999 compiled publishedand unpublished d data and calculated PCO forcc 2

68 paleosol sites. Many variables were standardizedto facilitate more direct comparison among the sites.

Ž .A value for S z of 5000 ppmV was uniformlyŽ .applied, which given our poor understanding of S z

is not unreasonable, but surely significant variationŽ .in S z existed among the 68 sites.

4.4. Estimating d , d , and df a s

Ž . 13According to Eq. 30 , the d C of soil-respiredŽ .CO d must also be estimated. This value differs2 f

Ž .from soil CO d by both the 4.4‰ diffusional2 s13 12 Žfractionation between C and C Craig, 1953;

.Cerling et al., 1991b and the relative input of heavy13 Ž .d . The d C of soil organic matter d appearsa om

Ž .roughly equal to its associated d Cerling, 1992b ,f

Žand can be taken as a direct proxy Cerling, 1992b;.Mora et al., 1991, 1996 . It is possible, however, for

differential decomposition, burial diagenesis, or con-tamination by modern organic matter to jeopardize

Ž .this equality Ekart et al., 1999 . It is important tomeasure d at each site, and not assume a constantom

Ž .value e.g., y24‰ , because excursions occur in theŽ .geologic record Bocherens et al., 1993; Jones, 1994 .

Accounting for d eliminates the argument that Com 4

plants or other unusually 13C-enriched organic matteris the cause for heavy d values, not elevated PCOcc 2Ž .Wright and Vanstone, 1991, 1992 . Unfortunately,organic matter is often rare in well-aerated soils

Žpertinent to this method Cerling, 1991, 1999; Mora.and Driese, 1999 , and some studies simply apply

today’s mean d for C plants to their fossil sitesom 3Ž .e.g., Lee, 1999 .

13 Ž .The d C of the atmosphere d is required bya

the model, but is one of the least sensitive variablesŽ .Cerling, 1992b . Typically, values are derived from

Ž . Žthe marine carbonate record d e.g., Veizer etocc.al., 1999 , assuming a constant fractionation and

Ž .ocean–atmosphere equilibrium but see Section 3.5 .The assumption of equilibrium may not be validduring intervals of rapid global change such as the

Ž .P–E boundary Ekart et al., 1999 . d has in turnaŽ .been used as a d proxy. Ekart et al. 1999 used aom

smoothed version of the d curve of Veizer et al.occŽ .1999 to infer d , and then assumed a constanta

fractionation of 18‰ between the atmosphere andŽ .organic matter D . While this procedure wasa – om

required to compare studies that had not measuredd with those that had, it nonetheless potentiallyom

introduces error, both because D may not bea – omŽ .constant and the smoothed Veizer et al. 1999 curve

does not accommodate for short-term d excursions.a

In addition, plants growing in the seasonably dry tosemi-arid regions conducive to pedogenic carbonate


formation are likely to be water stressed, which mayreduce D . Calculating d from d also greatlya – om om a

Ž .increases the sensitivity of the model to d Fig. 6 .a

This may be important for times where d is notocc

well constrained, such as the Permo-Carboniferous.Ž .PCO estimates of Ekart et al. 1999 during this2

interval decrease by 700 to 2500 ppmV when doccŽ .values from Popp et al. 1986 are used instead of

Ž . Ž .Veizer et al. 1999 Berner, unpublished data . Whenpossible, d should always be measured directly.om

The last parameter required to calculate PCO is213 Ž .the d C of the soil CO d . As discussed above2 s

Ž .Section 4.2 , since equilibrium is common betweend and d , and no other soil component significantlys cc

contributes to d , the d13C of pedogenic carbonatecc

is used as a proxy. This conversion involves a tem-Ž Ž ..perature-dependent fractionation Eq. 18 , and so

soil temperature must be estimated. This variable isnot well known, as it depends on air temperature,time of year of carbonate formation, soil texture, anddepth in profile. Seasonal temperature fluctuationsare dampened in soils at depth, and most pedogeniccarbonates form in the low-to-mid-latitudes. An esti-

Žmate of 258C is commonly used Cerling, 1991;.Mora et al., 1996; Ekart et al., 1999 ; however, one

could expect considerable variation. Calculations ofPCO based on soil temperatures of 208C versus2

Ž308C can differ by 700 to 1500 ppmV Cerling,.1999; Ekart et al., 1999 .

4.5. C plants4

The d of C plants is enriched f14‰ relativeom 4

to C plants, having a modern mean value of f3Ž .y12.5‰ Deines, 1980 . This large isotopic differ-

ence is reflected in d , and reinforces the need toccŽ .measure coexisting d Cerling, 1992a,b . If dom om

values indicative of C vegetation are found, how-4

ever, such sites should not be used for estimatingpaleo-CO . The d

13C gradient between d and C -2 a 4Ž .dominated d ca. 6‰ is much smaller than thatf

Ž .between d and C -dominated d ca. 20‰ , anda 3 f

thus the precision of PCO estimates based on C -2 4Ždominated sites is much poorer Cerling, 1984; Fig.

.7 . Evidence for C plants in pre-Neogene deposits4Žis sparse Cerling, 1991; but see Bocherens et al.,

.1993; Jones, 1994 , and so is not a critical issue forolder sites.

4.6. Choosing appropriate paleosols

Substantial literature exists pertaining to identify-Žing paleosols in the field e.g., Retallack, 1988,

.1990 . Common characteristics include clayskin-

13 Ž . 13Fig. 6. Sensitivity of PCO estimates to the d C of the atmospheric d when d is used to infer the d C of coexisting organic matter2 a aŽ . Ž . 13 Ž .d e.g., Ekart et al., 1999 . The two d C values of pedogenic carbonate d span most of the range currently observed in the fossilom cc

Ž . Ž . Ž .record. Note that the sensitivity increases with heavier d and lighter d i.e., at higher PCO . Lines drawn from Eqs. 18 and 31cc a 2Ž .assuming S z s5000 ppmV, soil temperatures258C, D s8‰, and D s18‰. Assuming a constant D , differences inocc – a a – om occ – a

Ž .published d values for the Permo-Carboniferous exceed 2‰ see Section 4.4 for discussion .a


Fig. 7. Difference in sensitivity of PCO estimates between pedogenic carbonate formed in pure C and C biomass systems. Lines drawn2 3 4Ž . Ž .from Eq. 31 assuming S z s4500 ppmV, D s9.0‰, d sy6.5‰, and d sy26% and y12‰ for C and C biomass,cc – s a f 3 4

respectively.

bounded peds, root traces, and evidence of bioturba-Ž .tion Cerling, 1992a, 1999 . Further analysis is re-

quired, however, to determine if a given paleosol isappropriate for this method. Although analyses ofd from modern soils show little input from detritalcc

carbonate, even for soil profiles developed on car-Ž .bonate parent material Quade et al., 1989 , it is wiseŽto avoid such soils Cerling, 1984; Ekart et al.,

.1999 . This is particularly important for paleosolslacking well-developed leached horizons above thepedogenic carbonates, as the d in such soils ares

Žoften influenced by detrital carbonate Cerling,.1992a, 1999 . Likewise, potential paleosols resting

on marine or lacustrine carbonates should be avoidedŽMora et al., 1991; Driese et al., 1992; Cerling,

.1999; Ekart et al., 1999 . Groundwater calcretes arealways to be avoided, as they do not form in adiffusion-dominated system. Such soils may showsigns of gleying, or contain massive carbonate de-posits, but can be difficult to distinguish from pedo-

Žgenic carbonates formed in unsaturated zones Cer-.ling, 1999 .

Carbonates that formed in soils with little biologi-Žcal activity e.g., before the Devonian colonization

.of vascular land plants should be treated with cau-tion, since their associated respiration rates were

Žundoubtedly very low Mora et al., 1991; Ekart et.al., 1999 , leading to inflated estimates of PCO . In2

addition, under such conditions carbonates are much

Žmore likely to form abiotically Mora et al., 1991;.Mora and Driese, 1999 .Ž .As discussed above Section 4.2 , it is crucial for

soils with moderate to high respiration rates to mea-sure d from )50 cm depth. Analyzing soils at toocc

shallow of a depth will lead to overestimation ofŽ .PCO . Mora et al. 1996 found that in paleo-verti-2

sols, which seasonally formed deep cracks, the dcc

of nodules were consistently heavier than the d ofcc

rhizoliths deeper in the profile. This may also high-light the need to sample deeper in vertic paleosolsdue to their associated greater penetration of atmo-

Ž .spheric CO Mora and Driese, 1999 .2

Burial diagenesis can potentially alter the dcc

signature. Most studies find no evidence for burialdiagenesis, however, even in recrystallized carbon-

18 Žates with large intra-site d O variability Cerling,.1991; Mora et al., 1996 . Nevertheless, micritic car-

bonate in the form of distinct nodules or rhizoliths ispreferable. Veins, coalballs, septarian nodules, and

Žradiating crystals are to be avoided Ekart et al.,.1999 .

4.7. Goethite method

An independent PCO proxy has been developed2

involving trace pedogenic carbonates containedŽ Ž . . Žwithin goethites Fe CO OH Yapp and Poths,3

. 131992, 1996 . In brief, the concentration and d C of


this goethite is a function of C) and d , respec-s s

tively, so that the atmosphere–goethite–organic mat-ter system can be modeled as simple mixing between

Ž .the two end members Yapp and Poths, 1992 :

d s d yd X rXqd 32Ž .Ž .g g Ža. g Žom . a g Žom .

where d sd13C of goethite, d and d s theg gŽa. gŽom.

theoretical d if only influenced by the atmosphereg

and organic matter, respectively, Xsmole fractionŽ .of Fe CO OH in the goethite, and X s the theoret-3 a

ical X if only influenced by the atmosphere.Thus, in a preserved soil profile, d will decreaseg

and X increase with depth, and they are inverselyŽ .related to one another Yapp and Poths, 1992 . This

relationship is insensitive to variations in soil pro-ductivity. If one plots 1rX vs. d , the slope termgŽw x .d yd X is related to PCO . If multiplegŽa. gŽom. a 2

measurements within a given profile are possible, theŽintercept term should be d Yapp and Poths,gŽom.

.1992 . Multiple measurements are often not possible,however, in which case the d

13C of coexisting or-Žganic matter can be taken as a direct estimate Yapp

.and Poths, 1996 . As in the analogous case of EkartŽ .et al. 1999 , d yd is assumed invariantgŽa. gŽom.

Ž Ž . .through time Yapp and Poths 1996 use 16‰ ,allowing for the calculation of X . As discusseda

Ž .above Section 4.4 , this assumption can be danger-ous. PCO , in turn, is related to X via Henry’s law.2 a

Although this model is rather sensitive to temper-Ž .ature Yapp and Poths, 1992 , published error esti-

Ž .mates for PCO ";1200 ppmV only account for2Ž .variability in d Yapp and Poths, 1996 . As withgŽom.

Ž .the model of Cerling 1984, 1991 , carbonate-con-taining soils that developed without a strong biologi-

Žcal component e.g., before the rise of vascular land.plants are prone to contain a non-biogenic fraction,

and should be treated carefully.

4.8. Summary

Ž .In the absence of C plants, S z , soil tempera-4

ture, and PCO are the most sensitive variables in2Ž .Cerling’s model Cerling, 1991, 1999 . Since soil

Ž .temperature and, in particular, S z are not wellconstrained, it is advisable to include as many soils

Žfrom geographically diverse sites as possible Cer-.ling, 1991, 1992; Mora and Driese, 1999 . When

Ž Ž ..PCO is low e.g., -10% of S z , its influence on2

C) is small, leading to imprecise PCO estimatess 2Ž . Ž .Cerling, 1992b . For example, Ekart et al. 1999estimated PCO from 15 modern soils to be 433"2

Ž .385 ppmV 1s . Thus, this proxy should not berelied upon when PCO -;1000 ppmV. This model2

Ž .also loses precision at high PCO see Fig. 5 , but2

the rate of loss is less than the other proxies, andshould be the proxy of choice when PCO is high2Ž .);1500 ppmV . The temporal range of thismethod also exceeds the other proxies, and should

Žyield reasonable estimates of PCO "500 to 10002.ppmV back to the Devonian, the time of rapid

vascular land plant colonization. Pre-Devonian esti-mates should be considered carefully since terrestrialbiological productivity was undoubtedly low.

Unfortunately, the temporal resolution of thismethod is the poorest of the proxies described here.Pedogenic carbonates typically form on the timescale

3 4 Ž .of 10 –10 years Cerling, 1984, 1999 , whichshould be considered the upper limit of the method’stemporal resolution. Studies wishing to quantifyPCO over shorter time intervals should use other2

proxies. In addition, this proxy should not be usedduring intervals with sharp isotopic excursions dueto potential disequilibria among the isotopic reser-

Ž .voirs Ekart et al., 1999 .

5. Stomatal density and stomatal index

Terrestrial plants obtain CO from the atmosphere2

for growth, and thus necessarily lose water vapor toan unsaturated atmosphere. The classical dilemmabetween carbon acquisition and water loss results in

Ž .the concept of plant water-use efficiency WUE ,which can be defined in a number of different ways.In the short-term of minutes, WUE is calculated asthe ratio of assimilation of CO by photosynthesis to2

Ž .loss of water by transpiration Stanhill, 1986 , de-scribed by:

g = p ypŽ .s a i

A1.6=PWUEs s 33Ž .g = e yeŽ . Es i a

Pwhere g is the stomatal conductance to water vapor,s

which is 1.6 times lower when considered as aconductance to CO , p and e are the partial pres-2 a a

sures of CO and water vapor, respectively, in the2


air outside the leaf, p and e are the partial pres-i i

sures of CO and water vapor, respectively, in the2

leaf air spaces and P is the atmospheric pressure.This definition simplifies to:

p ypa iWUEs 34Ž .

1.6= e yeŽ .i a

and emphasizes the importance of stomatal behaviorand morphology on the bi-directional control of CO2

and water vapor fluxes from the leaf. It should benoted in passing that timescales are of crucial impor-tance to plant WUE. On the longer timescale of aday, net assimilation will be less than expected byjust integrating assimilation rates during the wholeday, because respiratory loss of CO by non-photo-2

synthetic organs, and by leaves in darkness, must beŽaccounted for Farquhar et al., 1982; Farquhar and.Richards, 1984 . In addition, water loss may occur

Ž .through the leaf cuticle Jones, 1992 , a feature thatis rarely measured. A more complete definition ofWUE is therefore given by:

p yp = 1ywŽ . Ž .a i rWUEs 35Ž .

1.6= e ye = 1qwŽ . Ž .i a w

where w is the fraction of assimilates respired awayrŽ .by the plant and the term 1qw allows for tran-w

spiration through the cuticle.The WUE of plants over an entire growing season

includes plant respiratory carbon losses throughŽ .maintenance and synthetic respiration Jones, 1992

and whole-canopy transpiration calculated fromgrowth analyses:

W yWe 0k=

t y te 0WUEs 36Ž .

EdtHwhere W and W are the total dry weights of the0 e

plant at the beginning, t , and end, t , of the growing0 e

season, HEdt is the sum of daily transpiration and kconverts changes in dry matter to CO equivalents.2

This version of WUE is under variable control bystomatal behavior, depending on the coupling of the

Žcanopy with the over-lying air Jarvis and Mc-.Naugthon, 1985 .

Plant WUE, as defined in timescales of minutesŽ Ž . Ž ..Eqs. 34 and 35 , and for whole growing seasonsŽ Ž ..Eq. 36 , has been correlated with leaf stomatal

Ž . Ždensity SD at ambient CO Beerling and Wood-2.ward, 1996a , but plants tend to optimize carbon

Ž .gain per unit of water loss i.e., WUE through thefine control offered by regulating of stomatal open-

Ž .ing and closing Cowan, 1977 . In a CO -rich atmo-2

sphere, leaf WUE increases because CO induced2

partial stomatal closure reduces water vapor losseswithout reducing the CO -related stimulation of2

Ž .photosynthesis Morison, 1985 . An additional im-provement in WUE is possible in an elevated CO2

atmosphere by reducing the number of stomatal poresŽ . Žstomatal density, SD on the leaf surface Wood-

.ward, 1987; Woodward and Bazzaz, 1988 . Changesin SD can have an important effect on plant fitnessby influencing the growth response of whole plantsŽKundu and Tigerstedt, 1999; Hovenden and Schi-

. Ž .manski, 2000 . Woodward 1987 and WoodwardŽ .and Bazzaz 1988 demonstrated that atmospheric

ŽCO can regulate stomatal formation Beerling and2.Chaloner, 1992 and subsequent studies have shown

the inverse relationship between stomatal densityŽ .SD and PCO to be widespread across different2

Ž .taxonomic groups Beerling and Woodward, 1996bpointing to its potential to offer a plant-based paleo-CO sensor using fossil leaves that extends back2

through geological time. We emphasize that at theŽ .present the underlying genetic mechanism s linking

CO and SD remains to be identified and so the2

relationship must be regarded as correlative, notcausative.

This section describes important considerationsregarding the use of stomatal measurements on fossilleaves to detect paleo-CO signals. For details of2

fossil leaf cuticle preparation, and methods for stan-dardizing stomatal counts made on leaf surfaces,

Ž .etc., see Jones and Rowe 1999 .

5.1. The concept and use of stomatal index

To interpret paleo-CO signals from fossil leaves,2

there is need to control for other features of theenvironment that might influence their stomatal char-

Ž .acters Beerling, 1999 . Given that plants tends tooptimize their WUE, it follows that water stresswould be expected to reduce transpirational waterlosses, and this is usually brought about through

Žpartial stomatal closure in response to drought e.g.,.Clifford et al., 1995 . It is interesting to note that,

paradoxically, SD typically increases under


Ždroughted conditions Salisbury, 1927; Beerling,.1999; see Ticha, 1982; Royer, 2001 for reviews´

because of a reduction in epidermal cell size causingthe stomata to be packed closer together. However,under these circumstances, the stomata are nearlyclosed and the leaf angle relative to the sun is lower,both of which reduce transpiration water losses.

Ž .Salisbury 1927 introduced the concept of stom-Ž .atal index SI to remove the effects of drought,

calculated as follows:

SDSI % s =100 37Ž . Ž .

SDqED

where SD and ED are, respectively, stomatal densityŽ .and epidermal cell density. Eq. 37 shows that

effectively SI is the proportion of epidermal cellsŽthat are stomata where stomata are defined as the

.stomatal pore and two flanking guard cells . It istherefore independent of epidermal cell size andmeasures stomatal initiation and development, and isnot affected by subsequent cell expansion. Unlike

ŽCO Woodward, 1987; Woodward and Bazzaz,2.1988 , there is no experimental data demonstrating

Žthat water stress influences stomatal initiation Salis-bury, 1927; Sharma and Dunn, 1968, 1969; Estiarte

.et al., 1994; Clifford et al., 1995 .A recent review of the effects of irradiance, tem-

perature, vapor pressure deficit and water supply onleaf SD and SI concluded that SI has the fortuitousproperty of being relatively insensitive to all of thesebut sensitive to atmospheric CO levels, whereas SD2

can be influenced by each factor separately or inŽ .combination Beerling, 1999 . Such considerations

clearly indicate that SI rather than SD should bemore secure for interpreting paleo-CO variations2

from fossils. We recognize, however, that epidermalcells can become difficult or impossible to accuratelycount on poorly preserved fossil cuticles and this inturn requires the use of SD, but with a suitable

Žmeasure of caution Beerling et al., 1993; McElwain.and Chaloner, 1996 .

An important and often over-looked considerationin the relationship between SDrSI and CO is what2

stomatal developmentrinitiation is responding to.Careful experimental work has shown that plantshave the capacity to respond to a reduction in thepartial pressure of CO by an increase in leaf SI2Ž .Woodward and Bazzaz, 1988 . The response,

though, is insensitive to changes in the mole fractionŽ .of CO Woodward and Bazzaz, 1988 , indicating2

that the mechanism controlling SI and SD is sensi-Žtive to CO partial pressure and not mole fraction or2

.concentration . Since CO partial pressure falls with2

increasing altitude, but mole fraction is constantŽ .Gale, 1972 , these experimental observations largelyexplain the general trend of increasing SD of trees

Žand shrubs with altitude Korner et al., 1986; Wood-¨.ward, 1986 . From this, therefore, it follows that

fossil leaves showing changes in SDrSI though timeare actually recording ancient variations in atmo-spheric CO partial pressure. For leaves obtained2

from sites at altitudes close to sea level, the partialpressure of CO is approximately equivalent to CO2 2

concentration; quantitative CO partial pressure re-2

constructions from SDrSI measurements can there-fore be readily converted to units of CO concentra-2

tion. However, for paleo-CO reconstructions using2

fossils from sites at significant altitude, such a con-version requires the difficult-to-test assumption that

Žtotal atmospheric pressure has not changed cf..Rundgren and Beerling, 1999 . Clearly, it is advis-

able to control for paleoaltitude during the design ofinvestigations aiming to reconstruct paleo-CO varia-2

tions with this technique.

5.2. Canopy-scale considerations

Due to canopy photosynthesis and plant and soilrespiration, the CO concentration experienced by2

leaves within a canopy can deviate from the globalŽambient value Bazzaz and Williams, 1991; Buch-.mann et al., 1996 . This, in turn, may introduce bias

in PCO estimates from the SDrSI measurements2

made on fossil leaves if derived from a denseclosed-canopy where the PCO values at the time of2

stomatal development in the leaf were very differentfrom ambient. Atmospheric data from Harvard For-est in north central Massachusetts, USA, indicatethat CO concentration differences between the am-2

bient atmosphere and close to the ground surfaceŽ .4.5 m can be as large as 35 ppmV, especiallyduring the summer when soil and plant respiration

Ž .rates are high Fig. 8 . However, since bud formationand bud-burst by deciduous trees typically occurs inthe spring and fall when CO differences between2

the ambient atmosphere and canopy are -10 ppmV


Fig. 8. Canopy CO relative to ambient CO for four heights within a tree canopy in 1996. Canopy height is ca. 24 m. Ordinate represents2 2Ž .7-day running average of daily averages of hourly measurements at each height ns5311 for each height . Measurements at 29.0 m height

Ž .taken as ambient value mean for time interval at this heights370 ppmV . Raw data available at http:rrwww.as.harvard.edurchemistryrhfrprofilerprofile.html, and used with permission of S. Wofsy.

Ž .Fig. 8 , this effect by itself is unlikely to stronglybias paleo-CO trends.2

For tropical forests, it is important to note that thepotential for a forest canopy to become uncoupledfrom the over-lying atmosphere, and therefore alterthe local CO environment, is strongly dependent2

upon the regional meteorology and geographical lo-Ž .cation cf. Grace et al., 1995 . Leaf life spans and

primary production in tropical evergreen trees tendsto occur continuously so that a single canopy com-

Žprises of a range of cohorts e.g., Reich et al., 1991;.Clark et al., 1992; Williams-Linera, 1997 that po-

tentially developed at different CO concentrations.2

This suggests that the use of fossil leaves fromstratified ancient Mesozoic and Tertiary tropicalforests for paleo-CO signals may be more suscepti-2

ble to errors arising from within canopy PCO fluc-2

tuations; for tropical Amazonian forests, withincanopy PCO values are 30% higher than the global2

Ž .value Grace et al., 1995 .A more important effect of canopy development

is the logarithmic attenuation of irradiance withcanopy depth, described by Beers’ Law as:

Is I =eyk L 38Ž .0

where I is the photosynthetically active irradiance0

incident on a canopy, I is the irradiance beneath aleaf area index L, and k is the extinction coefficient

Ž .for irradiance typically 0.5 . This effect results inthe development of so-called sun and shade leavesŽ .Givnish, 1988 with differing SD values; SI values

Žremain largely conservative Salisbury, 1927;.Kurschner, 1997; Wagner, 1998 . It might be envis-¨

Ž .aged therefore that SD and possibly SI determina-tions from fossil leaf assemblages constituting amixture of sun and shade leaves might introduce a

Ž .bias resulting from this effect Poole et al., 1996 .There is some hope that such a bias is minimized inthe fossil record. Studies on the transport processesresponsible for sorting leaf material prior to fossiliza-tion indicate a preferential selection of sun morpho-

Ž .types Spicer, 1981 and in this context, carefulconsideration of the depositional environment is re-quired.

It is interesting to speculate that these two fea-Ž .tures CO and irradiance of the environment al-2

tered by canopy development might be expected tolead to evolutionary differences in the absolute stom-atal density of understory herbs and trees, as pro-

Ž .posed nearly 70 years ago by Salisbury 1927 . A


re-analysis of his data, accounting for the effects oftaxonomic relatedness, revealed that in fact treespecies typically have higher stomatal densities than

Ž .herbaceous species Kelly and Beerling, 1995 , al-though as expected marginal herbs had significantlyhigher stomatal densities than understory herbs. Interms of their responsiveness to CO increases, both2

recent historical and experimental, no strong correla-tions between stomatal density and growth formŽ .woody vs. non-woody; trees vs. shrubs , habitatŽ .cool vs. warm , or taxonomic relatedness have been

Žreported Woodward and Kelly, 1995; Beerling and.Kelly, 1997 .

5.3. Temporal sensitiÕity of stomatal responses toCO change2

The inverse relationship between SI and atmo-spheric CO has been reported as non-linear at CO2 2

Žconcentrations above ambient Woodward and Baz-.zaz, 1988; Kurschner et al., 1997 , although between¨

the range 250–370 ppmV most species typicallyŽ .show a linear response Fig. 9 . Indeed, a literatureŽ .survey of 65 SI responses from a pool of 35 species

Žto experimental CO enrichment usually 2= ambi-2.ent reported that 29% of cases showed a reduction,

with 66% showing no significant response, and the

Ž .remaining 5% showing an increase Royer, 2001 .SD responses followed a similar pattern. In thesestudies, the median length of exposure to an instanta-neous step increase in atmospheric CO concentra-2

tion was 45 days. However, analysis of the responseof SD and SI on fossil leaves spanning the last 400m.y. to CO concentrations above ambient, as deter-2

mined from independent PCO proxies and long-term2

geochemical models, indicates an inverse linear rela-Ž . Žtionship Fig. 10 Beerling and Woodward, 1997;

.Royer, 2001 . The data from fossils therefore inti-mate that the apparent ‘ceiling’ CO concentration to2

which SDrSI respond is mutable and that givensufficient time to adapt, plants have the capacity torespond to above ambient CO concentrations. The2

implication is that the stomatal method of paleo-CO2

estimation could potentially detect CO increases2

above ambient despite the apparent non-linear re-sponse shown by modern genotypes.

The reason for the apparent insensitivity in overhalf the species studied to date in short-durationexperiments is not known, but may be related to the‘ceiling’ to which modern genotypes have becomeadapted over the past ;2 m.y. of glacial–intergla-

Žcial CO fluctuations Woodward, 1987; Beerling2.and Chaloner, 1993 . If the linkage between PCO2

and stomatal initiation is genetically based, it might

Fig. 9. Stomatal index response of five species to PCO . Data compiled from herbarium sheets and altitudinal transects. Sources are as2Ž . Ž .follows: Ginkgo biloba and Metasequoia glyptostroboides Royer, unpublished data ; Betula pendula Wagner et al., 1996 ; Quercus

Ž . Ž .petraea Kurschner et al., 1996 ; Salix herbacea Rundgren and Beerling, 1999 .¨


Ž .Fig. 10. Response of stomatal density measured on fossil leavesraxes to atmospheric CO variations over the Phanerozoic rs0.74 .2Ž . Ž . Ž .Redrawn from Beerling and Woodward 1997 with additional data from Cleal et al. 1999 and Edwards 1998 . CO data from Berner2

Ž .1994 .

involve a time lag. The possibility of a genetic basisis intimated by transplant experiments with the up-

Žland grass Nardus stricta Woodward and Bazzaz,.1988 and analysis of plants growing near natural

Žhigh CO springs for many generations Beerling2

and Woodward, 1997; Bettarini et al., 1997, 1998;Fernandez et al., 1998; Paoletti et al., 1998; Tognetti´

.et al., 2000 . In a reciprocal transplant experiment,plants of the herbaceous species Tussilgao farfaracollected close to a geothermal spring in Italy, knownto have grown under elevated CO concentrations2

for many decades, and those from control ambientCO sites, were grown in controlled environments at2

Ž . Ž .ambient 350 ppmV and elevated 700 ppmV CO2Žpartial pressures for two years Beerling and Wood-

.ward, 1997 . The results indicated greater reductionsin SI under full irradiance conditions by plants fromthe high CO source, compared to those from the2

ambient CO source, providing some evidence for2

genetic adaptation between different plant popula-tions. The response is not, however, seen universally

Žin plants from high CO springs Bettarini et al.,2.1998 , although in an extreme case, plants of Spati-

phylum cannifolium and Bauhinia multinerÕia grow-ing at CO concentrations of up to 27,000–35,0002

ppmV in a natural cold CO spring in Venezuela2

were reported to have lower SI values by 70–80%

compared to their ambient CO grown counter parts2Ž .Fernandez et al., 1998 .´

Ž .Whatever the mechanism s , we note that theunknown duration of exposure required for a plant toadjust its SDrSI value to a high CO regime would2

appear to define the stomatal paleo-CO method’s2

temporal resolution. For most studies on fossil plantsencompassing tens of thousands to millions of years,and therefore many generations of even long-livedtrees, it seems reasonable to assume any geneticallydetermined ‘ceiling’ could be altered.

A further important issue relating to this methodis the strength of response, i.e., the magnitude of SIchange for a given unit of CO change. Two analy-2

ses on a life form basis have concluded that thedegree of reduction in stomatal density to CO en-2

richment increases with the initial stomatal densityŽWoodward and Kelly, 1995; Beerling and Kelly,

.1997 , defined by the relationship:kSD sSD yexp 178= ln SD 39Ž . Ž .Ž .E A A

where SD and SD are the stomatal densities atA E

ambient and elevated CO concentrations, respec-2

tively, and k is the slope of the major axis leastsquares regression resulting from independent con-

Žtrasts see Woodward and Kelly, 1995; Beerling and.Kelly, 1997 . The relationship is presented with the


caveat that it was derived mainly from short-termstudies, with a few samples from studies spanningdecades to centuries. As yet, there are insufficientdata for similar analyses on SI responses.

Ž .The response of SD predicted by Eq. 39 isŽ .shown graphically in Fig. 11 for three cases: 1 the

SD change predicted from analysis of results fromherbarium studies and CO enrichment experiments2Ž . Ž .ks0.348 , 2 the change if only results fromexperimental CO enrichment studies are included2Ž . Ž . Ž .ks0.417 Woodward and Kelly, 1995 and 3 thechange predicted from a study of SD changes in

Ž . Ž .Fig. 11. Generalized relationship between the initial stomatal density of a leaf grown at ambient CO amb and a the loss of stomata from2Ž . Ž .that leaf after growth with CO enrichment and b expressed as the proportion of stomata lost at high CO . Calculated from Eq. 39 based2 2

Ž . Ž .on analyses of herbarium and CO enrichment studies ks0.348 , CO enrichment studies only ks0.417 and the response of a2 2Ž .woodland flora to the past 70 years of CO increase ks0.260 .2


British woodlands to the past 70 years of CO2Ž . Ž .increase ks0.26 Beerling and Kelly, 1997 . It

can be seen that across all cases, plants tend todispense with between 10 and 50 stomatarmm2 in

Ž .an elevated CO atmosphere Fig. 11a , constituting2

a loss of between 30% and 10% of their originalŽ .density Fig. 11b . The relationships imply that there

is a maximum number of stomata that can be lost;leaves cannot function effectively without stomata,and this has led to the suggestion that in the short-

Žterm response curve that is sigmoidal van der Burgh.et al., 1993; Kurschner et al., 1997 . The exceptions¨

to this statement are some amphibious species suchŽ .as Littorella uniflora Nielsen et al., 1991 and

Ž .Lobelia dortmanna Pedersen and Sand-Jensen, 1992that function with no stomata at all.

Ž .These responses Fig. 11 relate to the study offossil materials because extant groups of plants mayhave SDrSI values reflecting the atmospheric CO2

Žpartial pressure at their time of origin Beerling and.Woodward, 1996b . For example, gymnosperm lin-

eages evolved during times of perceived high PCO2

and in general have low SI values today; conse-quently this minimizes potential for further reduc-tions in SI above present-day PCO . On this basis,2

we suggest it is important to consider the absoluteSD and SI values for a species targeted for study asthis gives a likely assessment of its potential sensitiv-ity of paleo-CO change. This suggestion probably2

holds regardless of duration of exposure because offunctional considerations required for effective pho-tosynthetic CO uptake and the generation of a2

transpiration stream.

5.4. Applications of stomatal method to detection ofpaleo-CO change2

Application of stomatal indices as a PCO proxy2

involves many fewer assumptions and calculationsŽthan the other proxies described here Sections 3, 4,

.and 6 . One simple approach involves tracking rela-tive temporal trends in SD or SI of a single speciesŽBeerling, 1993; Beerling et al., 1993; van de Wateret al., 1994; McElwain et al., 1995; Cleal et al.,

.1999 . Only qualitative trends in PCO can be de-2

duced in this manner. Quantitative paleo-CO recon-2

structions can be made by establishing an SI–CO2

relationship with known PCO , and then using this2

‘calibration set’ to estimate PCO from the SI of the2

same species from the fossil record. Standard curvesgenerated in this way have to date been derived froma mixture of herbarium data and data from plants

Žgrowing across altitudinal gradients e.g., Rundgren.and Beerling, 1999; see Fig. 9 . Experimental data

could also be used to develop training sets for usewith pre-Quaternary fossil leaves but in many casesexperimental growth conditions are very differentfrom those experienced by plants in the field andsome cross calibration is required, e.g., by compar-ing the SI values of leaves grown at ambient CO2

partial pressures experimentally and naturally, beforecombining the datasets.

A detailed quantitative paleo-reconstruction ofchanges in the partial pressure of atmospheric CO2

over the last 9000 ka of the Holocene using fossilleaves of Salix herbacea has been made by Rund-

Ž .gren and Beerling 1999 . These authors recon-structed CO values from SI measurements made on2

fossil leaves by developing a modern training set ofSalix herbacea SI values plotted against referenceCO partial pressures that were largely independent2

Ž .of ice core data. Their results Fig. 12a closelymatched the pattern of changes in atmospheric CO2

concentration documented from the ice core recordŽ . Ž .Fig. 12b Indermuhle et al., 1999b , providing in-¨dependent support for the notion that small changesin atmospheric CO can be sustained despite the2

relative stability of the global climatic conditionsŽ .Ciais, 1999 . This detailed, well-dated study pro-vides the strongest validation for the SI-based CO2

proxy to date and points the way for obtainingquantitative CO reconstructions for the Cretaceous2

and Paleogene, if a taxon has a sufficiently longfossil record, and has closely related extant represen-tatives amenable to CO -enrichment experiments.2

There are probably no extant stomata-bearing plantspecies that extend back to the pre-Cretaceous. Par-ticularly useful though are so called ‘living fossil’plants, e.g., Metasequoia glyptostroboides andGinkgo biloba, a term coined by Darwin to describeextant taxa belonging to lineages characterized bylittle or no phenotypic change since the MesozoicŽ .Beerling, 1998a . One possible problem in usingthese taxa to reconstruct paleo-CO changes in the2

past is that the calibration dataset will necessarilyhave been obtained from herbarium studies and ex-


Ž . ŽFig. 12. Holocene reconstructed variations in a the partial pressure of atmospheric CO using fossil Salix herbacea leaves after Rundgren2. Ž . Ž .and Beerling, 1999 and b measurements of atmospheric CO from ice cores after Indermuhle et al., 1999b .¨2

periments with modern genotypes that might show anon-linear response at CO concentrations above2

ambient. This would limit the ability of the methodto accurately reconstruct high PCO values.2

Considerable care is required in developing train-ing sets for the purpose of paleo-CO reconstruc-2

tions, and every effort should be made to obtainmaterials from a wide range of plants with differentgenotypes and growing in a variety of different

Ž .environments Birks et al., 1999 . A recent study ofthe early Holocene illustrates the difficulties that canarise when these considerations are neglected. Wag-

Ž .ner et al. 1999 presented a paleo-CO reconstruc-2

tion for the early Holocene, using a training setŽbased on historical SI changes from birch Betula

.pubescens, B. pendula trees growing at a single site,and the approach yielded values of 240–360 ppmV.These values were consistently 50–100 ppmV higher


than concentrations measured in ice coresŽ .Indermuhle et al., 1999a or reconstructed from¨

Žfossil Salix herbacea leaves Beerling et al., 1995;.Rundgren and Beerling, 1999 . Independent studies

of the response of SI in B. pubescens and B. pen-dula indicate that these taxa are rather insensitive tochanges in CO partial pressure with altitude, and2

increases in the atmospheric CO concentration be-2Ž .tween 1877 and 1978 Birks et al., 1999 . The

discrepancy appears to relate to the construction of amodern calibration dataset without paying sufficientattention to the natural variability of leaf cellularproperties of Betula trees.

A qualitative approach to estimating changes inpaleo-CO in the distant past, independently of the2

need for calibration datasets, is the use of the stom-Ž . Žatal ratio SR concept McElwain and Chaloner,

.1995 . SR is defined as the ratio of the SI of theŽ .Nearest Living Equivalent NLEs taxon to the fossil

Žto that of the fossil plant under investigation Mc-.Elwain and Chaloner, 1995 . NLEs are defined as

the nearest ecological and morphological equivalentin modern floras to the fossil plant under considera-tion. Note that the concept is related to, but distinct

from, the Nearest Living Relative approach. Takenas absolute ratios, the picture that emerges fromdetailed analyses of Devonian, Carboniferous, Per-mian, Jurassic and Eocene fossil plants, and their

ŽNLEs McElwain and Chaloner, 1995, 1996; McEl-.wain, 1998 , is that the SR shows a pattern of

response through geological time that mirrorsPhanerozoic CO trends predicted from mass bal-2

ance considerations of the long-term carbon cycleŽ .Fig. 13 . In an effort to make the SR methodsemi-quantitative, calculated values have been lin-early scaled with the output of Berner’s GEOCARB

ŽII model e.g., an SR value of 2 converts to a PCO2. Ž .of 2=pre-industrial value McElwain, 1998 . Al-

though useful to a certain extent, the problem withthis development is that it fails to provide a methodof paleo-CO estimation independent of the models.2

5.5. Summary

The precision in PCO estimates via stomatal2

indices is the highest of any current proxy. Whenherbarium-based standard curves are inverted, the95% confidence intervals for PCO predictions fall2

Ž .Fig. 13. Comparison of model predictions of atmospheric CO over the Phanerozoic from Berner and Kothavala, 2001 and stomatal-based2Ž . Ž . Ž .estimates. Stomatal ratio data unmarked filled boxes from McElwain and Chaloner 1995, 1996 and McElwain 1998 . Stomatal index

Ž . Ž . Ž .data ‘v’ from van der Burgh et al. 1993 . RCO units ratio of atmospheric CO in the past relative to the pre-industrial value of Berner2 2Ž .and Kothavala 2001 converted to PCO assuming a time-averaged pre-industrial value of 250 pmmV, which is roughly the mean PCO2 2

Ž . Ž .over at least the last 400 ka Petit et al., 1999 . Middle line represents the Abest estimateB predictions of Berner and Kothavala 2001 , whilethe two straddling lines represent error estimates based on sensitivity analyses.


Žbetween "10 and "40 ppmV van der Burgh et al.,1993; Kurschner et al., 1996; Rundgren and Beer-¨ling, 1999; Wagner et al., 1999; Royer, unpublished

.data . Thus, this method is preferable for time peri-ods when paleoatmospheric CO was roughly similar2

to present-day levels. When combined with experi-mental data, the method can be applied to timeperiods with elevated PCO . At some level of ele-2

vated PCO , however, SI responses of modern geno-2Ž .types may have lowered sensitivity see Section 5.3 ,

resulting in larger error envelopes. This CO satura-2

tion level has been observed at around 340 ppmVŽ .from some species Woodward and Bazzaz, 1988 ,

but also frequently to concentrations similar to theŽ . Žphytoplankton proxy 750–1250 ppmV Woodward

.and Kelly, 1995; Kurschner et al., 1997 .¨This method probably cannot be applied to pre-

Cretaceous sites due to its species-specific natureŽ .Section 5.4 . For pre-Cretaceous sites, the qualita-tive stomatal ratio technique of McElwain and

Ž .Chaloner 1995 can be applied. Relative changes inSD and SI within a given sequence, which also does

Žnot require extant species, can be illuminating e.g.,.Cleal et al., 1999 . The temporal resolution of the SI

method can be very high. While multi-million yearhigh-resolution data are not possible as with thephytoplankton method, short-term high-resolutiondata are widely available. Thus, this method is ideal

Žfor resolving potential rapid PCO changes e.g.,2.K–T boundary, P–E boundary . For example, using

Ž .the stomatal ratio method, McElwain et al. 1999documented a large PCO spike across the2

Triassic–Jurassic boundary at two fossil sites. Addi-tionally, in contrast to the stable isotope-based prox-ies, the SI method is insensitive to isotopic disequi-libria among the biospheric reservoirs, a potentialfactor during times of rapid global change.

6. d11 B of marine calcium carbonate

Dissolved boron in the oceans exists primarily asŽ . Ž .yB OH and B OH , and these two species differ in3 4

their ratio of the boron isotopes 10 B and 11 B. FieldŽobservations and experimental studies Hemming and

.Hanson, 1992; Sanyal et al., 1996 have shown thatthe uptake of boron into biogenic calcium carbonate

Ž .yrecords the isotopic composition of B OH with4

little isotopic discrimination. Because the relativeproportions of the two dissolved boron species varywith pH, and the degree of isotopic fractionationbetween the two species is known, the 11 Br10 B ofŽ .y ŽB OH also varies with pH Hemming and Hanson,4

.1992; Sanyal et al., 1996 . If the boron incorporatedinto fossil calcareous organisms faithfully records

Ž .ythe isotopic composition of B OH in paleo-4

seawater, it is possible to calculate the value of pHfor ancient oceans, once proper corrections for tem-

Žperature have been made Spivack et al., 1993; Sanyalet al., 1995, 1996; Palmer et al., 1998; Pearson and

.Palmer, 1999, 2000 . From paleo-pH, making certainassumptions about the behavior of dissolved carbonin seawater, one can calculate paleoatmospheric CO2

from paleo-pH and an assumed value for total dis-Ž .solved inorganic carbon DIC in seawater. This is

the basis for the boron isotopic method for estimat-ing paleo-CO . Estimates of CO levels ranging2 2

from the Paleocene to the Pleistocene using thismethod have been made by Pearson and PalmerŽ .1999, 2000 .

6.1. Method of calculation

Calculation of the value of pH from boron iso-topic data rests on a mass balance expression forboron isotopes and an equilibrium expression forŽ . Ž .yB OH and B OH . For isotopic mass balance:3 4

d Xqd 1yX sd 40Ž . Ž .B4 B3 SB

w Ž .yx Žw Ž .yx w Ž . x.where Xs B OH r B OH q B OH , d4 4 3 B411 Ž .y 11 Ž .sd B of B OH , d sd B of B OH , d s4 B3 3 SB

11 Žw Ž .yxd B of total dissolved boron B OH q4w Ž . x.B OH , and brackets represent molar concentra-3

tions. The equilibrium expression for borate chemi-Ž .cal equilibrium is in terms of X :

w x w qx w xX H r 1yX sK 41Ž .B

where K s the equilibrium constant in seawater.BŽ . Ž . Ž .Combining Eqs. 40 and 41 to eliminate X :

w qxH sK d yd r D y d ydŽ . Ž .Ž .B SB B4 B SB B4

42Ž .

Žwhere D sd yd fractionation between dis-B B3 B4.solved species . The method, in its simplest form,

assumes that d and D are constants, equal toSB B


present values, and that K can be calculated forBŽdifferent paleo-temperatures the small salinity varia-

tion for the open ocean should have a minimal effect.on K . Also, it is assumed that CaCO containsB 3Ž .yonly B OH that is taken up with either no frac-4

Žtionation Hemming and Hanson, 1992; Palmer et.al., 1998 or a known constant degree of fractiona-

tion D so that measurement of d11 B of CaCO isc 3

Ž .equal to D qd Sanyal et al., 1996 .c B4

To convert paleo-pH to paleo-CO further as-2

sumptions are necessary. A common assumption isŽ .that the total dissolved inorganic carbon DIC of the

Žoceans has not changed with time Pearson and.Palmer, 1999 . If true, then PCO is calculated from2

Žthe appropriate equilibrium expression corrected for.changes in temperature relating DIC, pH, and PCO2

and using the modern value for DIC. However, ifDIC has changed over time, then the calculatedresult for PCO can be greatly affected. To achieve2

more constrained PCO estimates, Pearson and2Ž .Palmer 2000 modeled changes in sea surface alka-

linity through time, which can also be used to con-vert pH to PCO . They predicted an overall decrease2

in alkalinity from 60 Ma to present day. This trendhas been independently corroborated using the d

44Caw 2qxof marine carbonates as a proxy for Ca , whichŽshould inversely relate to alkalinity De La Rocha

.and De Paolo, 2000 .

6.2. Problems with the method

Values of K and D are functions of tempera-B B

ture, so that in estimating paleo-pH correction for theeffect of changes in temperatures on these parame-ters needs to be made. This can be done for ancientenvironments where paleoceanographic data are

Žavailable e.g., Palmer et al., 1998; Pearson and.Palmer, 1999, 2000 . However, a more serious prob-

lem arises in assuming that d has remained nearlySBŽ .constant over time. Lemarchand et al. 2000 have

shown that the boron isotopic composition of theocean most likely has varied considerably over theCenozoic due to changes in the inputs and outputs ofboron to and from the oceans. For example, theyshow that the boron isotopic composition of present-day rivers varies by over 40‰ in d

11 B. Thus, changesin the relative proportions of riverine input from

Ždifferent sources over millions of years their esti-

mate of the mean residence time of B in seawater is.14 million years could alter oceanic B isotope com-

position to an extent greater than that resulting fromvariations in pH. Even holding the isotopic composi-tion of riverine input constant, Lemarchand et al.Ž .2000 show that Cenozoic changes in d could beSB

as much as 2‰ in 20 million years. A difference of2‰ is equivalent to a change in pH of 0.3 unitsŽ .Palmer et al., 1998 , which means a change inPCO of a factor of 2 to 4.2

Another problem arises from the assumption ofthe degree of fractionation of isotopes during theincorporation of boron in CaCO . Since fractionation3

during biological uptake has been demonstrated tovary among species due to vital effects, it is impor-tant to ascertain how this fractionation might varywith different organisms. Hemming and HansonŽ .1992 found little evidence for fractionation for avariety of modern calcareous organisms, but this was

Ž .not verified by Vengosh et al. 1991 who foundŽ .much larger variations. Sanyal et al. 1995, 1996 ,

based on experimental and field studies, found aconstant fractionation of about 4‰ for one foramspecies, Orbulina uniÕersa, but found no fractiona-tion for another foram, Globigerinoides sacculifer.

Ž .In the paleo-pH studies of Palmer et al. 1998 andŽ .Pearson and Palmer 1999, 2000 , it is assumed that

there was no fractionation for a variety of differentforam species; in other words, the boron isotopic

Ž .ycomposition of calcite represents that for B OH in4Žthe original seawater in the above notation they

.assume that D s0 . In the study of Pearson andcŽ .Palmer 1999 , support for this assumption is pro-

vided by the finding of essentially the same d11 B for

Ždifferent foram species from the same depth temper-.ature range. However, the variability for forams was

Ž .found to be greater up to 4‰ for a larger numberŽ .of samples in the study by Palmer et al. 1998 .

Diagenesis can bring about appreciable changes inthe boron isotopic composition of CaCO during3

Ž .burial. Spivack and You 1997 have convincinglydemonstrated this from the analyses of bulk carbon-ate in an ODP core from the eastern equatorialPacific Ocean. Here, they found that the d

11 B ofcarbonates ranged from y5.5‰ to 23‰ with themost negative values representing a totally recrystal-lized end member. In the same sediments, interstitialwaters showed much less variation in d

11 B with


depth because of diffusional and advectional ex-change with seawater.

Finally, there is the problem of calculating paleo-CO from paleo-pH. First of all, one must assume2

equilibrium of CO between that dissolved in the2

oceans and that present as a gas in the atmosphereŽ .see Section 3.5 . More important, it is not likely thatthe oceans have exhibited a constant level of DICover millions of years, as assumed in the calculations

Ž . Žof Pearson and Palmer 1999 but not in those of.Pearson and Palmer, 2000 . Carbon is continuously

supplied to the atmosphere and ocean by degassingfrom metamorphism and magmatism, and by theweathering of carbonate minerals and organic car-bon, and is continuously consumed by the production

Žof carbonate and organic carbon sediments Berner,.1999 . Hence, the total dissolved inorganic carbon

load of the ocean could be expected to vary overtime.

6.3. Summary

The boron isotope method provides an indepen-dent check on other paleoatmospheric CO methods.2

However, it is based on many assumptions that, ifnot correct, can lead to incorrect results. Before thismethod can be put into general use, it will benecessary to gain a better idea of the d

11 B of ancientoceans, how boron isotopes are fractionated duringuptake by various calcareous organisms, and howone can estimate the level of dissolved inorganiccarbon in ancient oceans.

7. Redox chemistry of marine cerium

Ž .Liu and Schmitt 1996 have devised a ratheringenious method, involving many equilibrium steps,for deducing paleo-CO levels from the concentra-2

tion of cerium in sedimentary rocks. Their method,however, rests upon many assumptions. Among oth-

Ž . 3qers, these include: 1 the reaction 4Ce qO q2

4Hqs4Ce4qqH O is at chemical equilibrium at2Ž .all times; 2 total dissolved Ce in seawater is ac-

counted for almost entirely by carbonate-complexedŽ .species; 3 the total dissolved inorganic carbon DIC

and alkalinity of seawater remains constant overŽ .geological time; 4 the level of dissolved oxygen

within the upper 600 m of the oceans does notŽ .change with time; 5 the activity coefficient of Ce in

sedimentary minerals remains constant over time.ŽAll of these assumptions and several others not

.discussed here have serious problems. MoffettŽ .1990 has shown that Ce oxidation is microbiallyaffected and that the redox couple in seawater is notexplained simply by equilibrium with O and H O.2 2

ŽCerium is a highly charged trace element abouty12 .10 M in seawater and could easily be complexed

Žwith many other species such as dissolved organic.matter other than carbonates. As is stated in the

Ž .section on the boron isotope method Section 6.2 , itŽ .is likely that DIC and alkalinity have varied con-

siderably over time. During several times in thegeologic past, the average O level in upper portions2

Žof the oceans could have varied considerably e.g.,.anoxic oceanic events during the Mesozoic . Finally,

it is not clear in what mineral form Ce was originallyŽpresent in any given sediment sample Liu and

.Schmidt analyzed carbonates and what were itssolid solution properties; so it is difficult to assumethat its thermodynamic behavior in the solid state hasbeen constant over time.

8. Phanerozoic CO trends: a comparison of2

methods

From this review of paleo-CO proxies, it is clear2

that different methods have different temporal reso-Žlutions i.e., the amount of time a single sample.integrates , and could be usefully viewed in a hierar-

chical series with the long-term carbon cycle modelsproviding the overarching set of predictions on atimescale of millions of years. Next, paleosol CO2

proxies provide coverage on a timescale of 103–104

Žyears the minimum time required for soil carbonates.to form , and these offer a broad crosscheck on the

mass balance model results. The two ocean CO2

proxies, phytoplankton carbon isotopes and boronisotopes, are limited by the resolution of the marinerecords that depend on factors such as burial rate,productivity, and intensity of bioturbation. A reason-able limit in temporal resolution for organic carbon

3 4 Žin pelagic sediments is 10 –10 year Kennett,.1982 . The terrestrial stomatal-based PCO indicator2

probably offers the best temporal resolution. In this


case, the temporal resolution of pre-Quaternary leaveswill typically be limited by the response time for agiven species, which can range anywhere betweenseveral months to 102 year. This gives the followingsequence of temporal sensitivity: mass balance-paleosols f phytoplankton s boron isotopes -stomata. This emphasis on timescales is importantbecause for a given method to detect a change in theconcentration of atmospheric CO , its response time2

needs to be less than an individual component of theglobal carbon cycle, i.e., turnover times of organicand inorganic carbon in the oceanic, atmospheric,marine and terrestrial components.

Other important temporal considerations are howwell an individual PCO estimate can be dated, and2

the availability of continuous sequences. In mostcases, the errors in absolute dating far exceed tempo-ral resolutions, and so the ability to compare PCO2

estimates from different localities is diminished. Ingeneral, however, marine-based proxies can be betterdated than terrestrial-based ones. Temporal trends in

ŽPCO are best captured in continuous or near con-2

.tinuous sequences. Again, very good sequences ex-ist in marine settings. For example, the average

Ž .sampling density in Pagani et al.’s 1999a,b se-quence was ;200 k.y., and in some settings it maybe possible to sample at or near the single-sample

Ž 3 4 .integration time ;10 –10 year . Sequences ofpaleosols are less common, and generally more tem-porally discontinuous. Sequences of plant assem-blages vary in temporal quality. For example, lacus-trine sequences can have annual resolution, but rarelypersist for great lengths of time.

Paleo-CO proxies also vary in their precision of2

PCO estimates. For geochemical models, the preci-2

sion of PCO predictions can only be assessed via2Ž .qualitative sensitivity analyses Section 2.2 . In theŽ .case of Berner and Kothavala 2001 , CO sensitiv-2

ity ranges from "75–200 ppmV for the Tertiary toŽ"1500–3000 ppmV for the early Paleozoic see

.Figs. 13–16 . The pedogenic carbonate proxy rangesin error from "400–500 ppmV for the Tertiary to"500–1000 ppmV for the mid-Paleozoic through

Ž .Mesozoic see Fig. 14 . PCO error estimates from2

Ž .Fig. 14. Comparison of model predictions of atmospheric CO over the Phanerozoic from Berner, 1994 and pedogenic carbonate-based2Ž . Ž .estimates including the goethite method . The shaded region represents the error estimates of Berner and Kothavala 2001 . RCO units of2

Ž . ŽBerner and Kothavala 2001 converted to PCO as in Fig. 13. Vertical lines represent 78 pedogenic carbonate-based PCO estimates data2 2

from Suchecky et al., 1988; Platt, 1989; Cerling, 1991, 1992a,b; Koch et al., 1992; Muchez et al., 1993; Sinha and Stott, 1994; Andrews etal., 1995; Ghosh et al., 1995; Mora et al., 1996; Yapp and Poths, 1996; Ekart et al., 1999; Elick et al., 1999; Lee, 1999; Lee and Hisada,

.1999 . The solid line is a five-point running average of the mean PCO of every estimate. This approach smoothes short-term CO2 2Ž .fluctuations and is more directly comparable with the model of Berner and Kothavala 2001 . The dashed line is a five-point running

Ž .average incorporating a recalculation of Ekart et al. 1999 data during the late Carboniferous and early Permian using the marine carbonate13 Ž . Ž .d C data of Popp et al. 1986 see Sections 4.4 and 8 for details .


Ž .Fig. 15. Comparison of model predictions of atmospheric CO over the last 60 Ma gray shaded area; from Berner and Kothavala, 2001211 Ž . Ž .and marine d B-based estimates black shaded area; from Pearson and Palmer, 2000 . RCO units of Berner and Kothavala 20012

converted to PCO as in Fig. 13.2

the d13C of phytoplankton range from "25–100

ppmV for the Tertiary to "150–200 ppmV for theŽ .Cretaceous see Fig. 16 . Above ;1000 ppmV, this

method loses its sensitivity. For stomatal indices,error estimates for the Tertiary are "10–40 ppmV

Ž .Royer, unpublished data; see Fig. 13 . Dependingon the plant species chosen, this method’s sensitivityto PCO diminishes at some point above 350 ppmV.2

Additionally, quantitative pre-Cretaceous estimatesare probably not possible due to the lack of long-

Ž .Fig. 16. Comparison of model predictions of atmospheric CO over the last 160 Ma from Berner and Kothavala, 2001 and marine organic213 Ž .matter d C-based estimates. Unmarked filled boxes from Freeman and Hayes 1992 ; geoporphyrins used as a biomarker. Open box from

Ž . Ž . Ž 13Pagani et al. 1999a,b ; C alkenones used as a biomarker. Box labeled AsB from Stott 1992 does not include estimates from P–E d C37:2. Ž .excursion . Middle line represents the Abest estimateB predictions of Berner and Kothavala 2001 , while the two straddling lines represent

Ž .error estimates based on sensitivity analyses. RCO units of Berner and Kothavala 2001 converted to PCO as in Fig. 13.2 2


ranging taxa. Thus, the phytoplankton and stomatalŽproxies should be relied upon for Tertiary and pos-

.sibly Cretaceous reconstructions, while the pedo-genic carbonate proxy yields the most useful CO2

estimates for the pre-Tertiary.

Despite the wide variety of assumptions made foreach method, a surprisingly coherent picture is

Žemerging of Phanerozoic PCO change see Figs.2.13–16 . The largest discrepancy exists between some

of the Paleogene estimates of Pearson and Palmer

Ž . Ž .Fig. 17. Changes in the a stomatal index and stomatal ratio of fossil Ginkgo and cycad taxa from Greenland, b ratio of atmospheric CO2Ž . Ž .in the past relative to the pre-industrial value RCO and calculated change in global temperature, and c calculated changes in leaf width2

with and without the reconstructed changes in CO and temperature and observed changes in leaf width across the Triassic–Jurassic2Ž .boundary from the Greenland fossils redrawn from McElwain et al., 1999 .


Ž .Fig. 17 continued .

Ž .2000 using the boron isotope method and the otherŽ .methods compare Fig. 15 with Figs. 13, 14 and 16 .

Ž .As discussed above Section 6.2 , however, theseboron-derived estimates are probably not well con-strained. Another discrepancy exists between the pe-

Ž .dogenic carbonate estimates of Ekart et al. 1999and the geochemical predictions of GEOCARB forthe late Carboniferous and early Permian, i.e., thelater stages of the Permo-Carboniferous glaciationŽ . Ž .see Fig. 14 . Ekart et al. 1999 used the marine

13 Ž .carbonate d C record of Veizer et al. 1999 topredict the d

13C of the pedogenic carbonate’s associ-ated organic matter. This procedure decreases the

Ž .precision of PCO estimates see Section 4.4 . The2

PCO discrepancy largely disappears if the d from2 occŽ .Popp et al. 1986 are used instead of Veizer et al.

Ž . Ž .1999 see Fig. 14 . Alternatively, the discrepancymay be an artifact of the differing temporal resolu-tions of the two methods. Unlike the GEOCARBmodel, the pedogenic carbonate proxy has the poten-

Ž 3 4 .tial to resolve short-lived 10 –10 year PCO2

excursions. If true, this example highlights the im-portance of considering temporal resolution whencomparing PCO estimates from multiple methods.2

Nevertheless, it is important to apply multiplePCO proxies for a given time interval. We might2

envisage, for example, the complementary use ofstomata and phytoplankton to detect CO changes2

across the K–T boundary or the P–E boundary.Similarly, the stomatal proxy might usefully be ap-plied across the Cenomanian–Turonian boundarywhere phytoplankton and terrestrial plant d

13C shiftshave indirectly identified a possible abrupt fall in

Ž .CO Kuypers et al., 1999 .2

9. Independent testing of paleo-CO estimates2

An important feature of the all of the methods ofpaleo-CO reconstructions reviewed here is the need2

to seek independent evidence for an associatedchange in climate. For the geochemical carbon cyclemodel predictions and paleosol estimates, times oflow global CO concentrations over the Phanerozoic2

generally coincide with episodes of major glaciationsŽ .Berner, 1998; Crowley, 2000 , with the exception ofthe Ordovician when the solar constant was some4–5% lower than now. Other indicators of globalclimate could also be deployed for this purposeŽ .Parrish, 1998 but are only rarely used. Instead, therecourse typically taken has been to compare PCO2


Žestimates between different methods Berner, 1998;.Ekart et al., 1999; Pearson and Palmer, 1999 .

Perhaps because the stomatal paleo-CO proxy2

approach is still in its infancy relative to most of theother CO proxies, and regarded as somewhat con-2

troversial, where changes in CO have been detected2

using this method more effort has been made to seekindependent evidence of global change from thegeologic record. For example, Neogene oscillationsin atmospheric CO inferred from changes in the SI2

of fossil oak leaves were found to correlate withclimatic records determined from fossil pollen records

Žin the Lower Rhynie Embayment van der Burgh et.al., 1993 . Low SI values, i.e., high CO episodes,2

correlated with warm climatic periods indicated fromthe fossil pollen assemblages. Reaching back further

Ž .into the geologic record, Cleal et al. 1999 tracked adecrease in the SD and SI of pteridiosperm Neu-ropteris oÕata fronds through the Westphalian andinto the Cantabrian of the Upper Carboniferous withthe inference atmospheric CO partial pressure rose2

through this time. These authors then found secureevidence that the postulated CO increase correlated2

with a decrease in the extent of glacial deposits inGondwana and the reduced burial of terrestrial or-ganic matter resulting from the loss of tropical wet-land forests. This example therefore provides a casewhere changes in fossil plant morphology yield aglobal signal of CO change of considerable antiq-2

uity.Recent work has shown that it is possible to

utilize the relatively rapid response time of the stom-atal CO method to detect abrupt CO changes, in2 2

Ž .particular across the Triassic–Jurassic T–J bound-Ž . Ž .ary 205.7 Ma McElwain et al., 1999 . The T–J

boundary is of interest because an absence of securemarine geochemical records of climate change at thistime means that the causes of this, the third largestextinction in the Phanerozoic, continue to remainuncertain. In this context, it is interesting to note thatthe timing of all of the major animal extinctionevents over the past 500 m.y. differs from that ofplant extinction events. Therefore, fossil plants arepotentially able to provide enlightening records ofenvironmental change during major faunal mass ex-tinction events.

Ž .McElwain et al. 1999 reported that the SI offossil Gingko and Cycad taxa showed marked reduc-

tions across the T–J boundary that were mirroredwhen stomatal ratios were calculated from SI mea-

Žsurements on their nearest living equivalents Fig..17a . Conversion of the SR values to PCO values2

indicated that the atmospheric CO concentration2

increased massively from ;700 to ;1600 ppmVacross the boundary with associated global

Ž .‘greenhouse’ warming Fig. 17b . This CO increase2

coincided with independent evidence for extensivevolcanic activity during the breakup of PangeaŽ .Marzoli et al., 1999 , and moreover, the quantity ofCO required to increase the atmospheric concentra-2

tion by this amount is well within that estimated tobe have been released during the production of floodbasalts of the Central Atlantic Magmatic ProvinceŽ .CAMP . The timing of the CAMP formation and itstemporal brevity, determined from 40Arr39Ar dating,support its possible involvement in the T–J boundary

Žextinction Marzoli et al., 1999; McElwain et al.,.1999 .

The fossil plants themselves also provide evi-dence for global climatic warming across the T–J

Ž .boundary McElwain et al., 1999 . Analysis ofchanges in the morphologies of fossil leaves downthrough the different plant beds in Greenland showthat the major floral turnover indicated by pollenanalysis was linked to the extinction of broad-leavedtaxa and the survival of those groups possessing

Žfinely divided or dissected leaf morphologies Fig..17c . Energy budget calculations for individual

leaves, based on several key physiological attributes,indicate that wide leaves with limited convectivecooling capacity, because of a low boundary layerconductance, would have quickly reached lethal tem-peratures for plants distributed at low paleolaltitudes,if the CO increase and global warming had actually2

Ž .occurred Fig. 17c . In contrast, if the CO and2

global temperatures increases implied by the stom-atal data were simply artifacts of the datasets, andboth had remained constant, then no selective pres-sures would have operated for any observed reduc-tion in leaf width to maintain their temperature be-

Ž .low lethal thresholds Fig. 17c . This integration ofstomatal-based paleo-CO estimates with indepen-2

dent data sources reinforces the view that globalatmospheric signals can be derived from plant fossilsand strengthens our confidence in the approach. Asnew approaches for interpreting changes in different


Žcomponents of the global carbon cycle emerge e.g.,.Haug et al., 1999 then it should be possible to

devise alternative means of testing proxy estimatesof PCO change against independent geologic data2

sources.

Acknowledgements

DLR and RAB were partially supported by DOEgrant DE-FGO -95ER14522. DLR also acknowl-2

edges support from a NSF Graduate Research Fel-lowship. DJB gratefully acknowledges fundingthrough a Royal Society University Research Fel-lowship and the Natural Environment Research

Ž .Council, UK award no. GR3r11900 . We thank S.Wofsy, B. Munger, M. Goulden, and C. Barford forproviding canopy CO data from Harvard Forest.2

We also thank L. Kump and W. Chaloner for con-structive comments.

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