PAUL F. HOFFMAN SERIES

A Temperature-DependentPositive Feedback on theMagnitude of Carbon Isotope Excursions

Seth Finnegan1,2, David A. Fike3,David Jones4, Woodward W. Fischer1*1 Division of Geological and Planetary Sci-ences, California Institute of Technology,1200 E. California Blvd., Pasadena, CA,91125, USA

2 Department of Integrative Biology, Univer-sity of California, 1005 Valley Life SciencesBldg #3140, Berkeley, CA, 94720, USA

3 Department of Earth and Planetary Sci-ences, Washington University, St. Louis,MO, 63130, USA

4 Department of Geology, 11 Barrett HillRoad, Amherst College, Amherst, MA,01002-5000, USA

* Corresponding Author:wfischer@caltech.edu

SUMMARYThe decrease in the average magnitudeof carbon isotope excursions in marinecarbonates over Phanerozoic time is alongstanding unresolved problem. Inaddition, carbon isotope excursions

commonly co-occur with oxygen iso-tope excursions of the same sign,implying the existence of a longstand-ing link between organic carbon burialfluxes and temperature. It was pro-posed that this connection was provid-ed by the thermodynamic relationshipbetween temperature and microbialrespiration rates – changes in tempera-ture drive changes in organic carbonremineralization rate and organic car-bon burial efficiency. Such a mecha-nism provides the logic for a positivefeedback affecting the magnitude ofboth climate changes and carbon iso-tope excursions. Here, we employfeedback analysis to quantify thestrength of this mechanism with modi-fications to a simple carbon isotopemass balance framework. We demon-strate that the potential strength of thisfeedback is large (perhaps several per-mil) for plausible ranges of historicalclimate change. Furthermore, ourresults highlight the importance of thesurface temperature boundary condi-tion on the magnitude of the expectedcarbon isotope excursion. Compar-isons of our model predictions withdata from the terminal Eocene andLate Ordovician (Hirnantian) green-house–icehouse climate transitions sug-gest that these excursions might besubstantially explained by such a ther-modynamic microbial respiration feed-back. Consequently, we hypothesizethat the observed pattern of decreas-ing excursion magnitude toward thepresent might be explained at least, inpart, by a decrease in the mean tem-perature of environments of organiccarbon burial driven by long-term cli-mate and paleogeographic trends.

SOMMAIRELa diminution de l'amplitude moyennedes excursions des isotopes du carbone

dans les carbonates marins au fil duPhanérozoïque est une énigme delongue date. On note en outre que lesexcursions des isotopes du carbonecoexistent couramment avec des excur-sions isotopiques de même signe del'oxygène, ce qui implique l'existenced'un lien de longue date entre les fluxd’enfouissement du carbone organiqueet la température. On a suggéré que celien découlait de la relation thermody-namique entre la température et lestaux de respiration microbienne - leschangements de température détermi-nent le taux de reminéralisation du car-bone organique et l’efficacité de l’en-fouissement du carbone organique.Un tel mécanisme peut expliquer larétroaction positive affectant à la foisl'ampleur des changements climatiqueset les excursions des isotopes du car-bone. Dans le cas présent, nous util-isons l'analyse de la rétroaction pourquantifier la robustesse de ce mécan-isme avec des modifications d’un sim-ple bilan de masse des isotopes du car-bone. Nous démontrons que larobustesse potentielle de cette rétroac-tion est forte (peut-être plusieurs pourmille) dans les gammes plausibles duchangement climatique historique. Deplus, nos résultats mettent en évidencel'importance de la condition aux limitesde la température de surface sur l'am-pleur de l'excursion isotopique du car-bone attendue. Les comparaisons desprédictions de notre modèle avec lesdonnées de la fin de l'Éocène et de lafin de l’Ordovicien (Hirnantien) destransitions climatiques à effet de serre-effet/de glaciation permettent depenser que ces excursions pourraientêtre correctement expliquées par unetelle rétroaction de la thermody-namique de la respiration microbienne.Par conséquent, nous émettons l'hy-pothèse que la tendance observée de

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diminution de l'ampleur de l’amplitudedes excursions du passé vers le présentpeut s'expliquer, au moins en partie,par une diminution de la températuremoyenne du milieu d'enfouissement ducarbone organique engendrée par destendances climatiques et paléogéo-graphiques à long terme.

INTRODUCTIONGeologically rapid excursions in thecarbon isotopic composition of marinecarbonates and organic matter (δ13Ccarb,δ13Corg, respectively) are a conspicuousbut still incompletely understood fea-ture of the stratigraphic record. Theδ13C trends record clear changes in thebehaviour of the carbon cycle, but mayreflect a variety of processes includingvolcanic activity, rock weathering, pri-mary production, and organic carbonpreservation; and many excursions like-ly record complex interactions betweencarbon cycle processes (Kump andArthur 1999). Nevertheless, somecommonalities can be observed thatcan help identify important, longstand-ing feedbacks.

Noting that Phanerozoic δ13Cexcursions commonly exhibit a positivecorrelation with δ18O excursions, Stan-ley (2010) suggested that many δ13Cexcursions were caused by climatechange via the thermodynamic linkagebetween ambient temperature and themetabolic rates of microbial decom-posers, using similar logic to biogeo-chemical models of marine productionexport efficiency (Laws et al. 2000).The idea is simple and useful: micro-bial respiration rates are strongly tem-perature-dependent, and so changes inocean temperatures affect the efficien-cy of organic carbon export and burial,and can thereby drive changes in δ13Cvalues. In this framework, climatecooling causes more efficient organiccarbon burial and positive δ13C excur-sions; climate warming has the oppo-site effect and would cause negativeexcursions (Stanley 2010). As noted byStanley (2010), this mechanism addi-tionally provides a potential explana-tion for the commonly observed coin-cidence of δ13C excursions with extinc-tion events in the fossil record.

One important aspect ofPhanerozoic δ13C excursions that Stan-ley (2010) was unable to fully explain isthe variation in their magnitudes over

Earth history. He noted that, “It is puz-zling, for example, that the terminal Eoceneexcursions were small despite having beenassociated with substantial global cooling.” Infact, the terminal Eocene excursion isone of the largest of the Cenozoicinterval, but it is comparatively small inthe context of Earth history. Indeed,one of the most striking features ofthe Phanerozoic carbon isotope recordis a decline in the average magnitude ofisotope ratio excursions through time(Grotzinger et al. 2011; Fig. 1). Here,we elaborate on Stanley’s (2010)hypothesis and draw attention to apossible explanation for the decrease inthe magnitude of δ13C excursionsobserved over Phanerozoic time.

We hypothesize that a keyaspect of the temperature– organiccarbon burial feedback is its sensitivityto the initial boundary condition: dueto the exponential nature of the rela-tionship between environmental tem-perature and metabolic rates (Fig. 2A),the expected magnitude of change inorganic carbon burial (and δ13C)depends not just on the sign and mag-

nitude of temperature change but also,critically, on the baseline temperaturefrom which temperature change initi-ates (hereafter referred to as initialtemperature). It is possible to modifyand employ simple isotope mass-bal-ance calculations to estimate the poten-tial effect strength (i.e. system gain)that this feedback might provide, andthen reflect on these estimates by com-parison to paleoclimate proxy data gen-erated from the fossil record. The rel-ative magnitudes of the terminalEocene and Late Ordovician carbonisotope excursions – two events thatrecord greenhouse–icehouse transitions– can be explained, in part, by proxy-based reconstructions of initial tem-perature and change in temperatureduring these events. Building on thisresult, we develop the hypothesis thatone possible explanation for thedecreasing magnitude of carbon iso-tope excursions throughout Phanero-zoic time is the lower temperatures oforganic carbon burial environmentsdue to the overall cooling trendobserved in proxies of seawater tem-

Figure 1. Boxplots showing carbon cycle behaviour through the Phanerozoic interms of the magnitude (absolute value of change, in permil) of δ13C excursions,binned into 50 million year intervals. Horizontal bars are medians, and boxesenclose the interquartile ranges (25th through 75th percentile), closed circles markoutliers. Data from Saltzman and Thomas (2012), with excursions defined as inGrotzinger et al. (2011).

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perature, and to net movement of con-tinents from tropical to temperate lati-tudes over this interval.

FEEDBACK ANALYSIS AND EFFECTSTRENGTHIt is useful to conceptualize the tem-perature-dependent organic carbonburial mechanism proposed by Stanley(2010) as a feedback in a dynamic sys-tem, rather than an external forcingmechanism, because many other fac-tors can drive and influence δ13C trendsin addition to climate (Jones andJenkyns 2001; Svensen et al. 2004;Tejada et al. 2009). Some δ13C excur-sions may record changes in total car-bon burial flux rather than merelychanges in the ratio of organic to inor-ganic carbon burial (Brenchley et al.1994; Saltzman and Young 2005), andin these cases climate changes may be a

Figure 2. Temperature dependenceof several important feedbacks onmarine organic carbon burial. A)Thermodynamic relationship betweenrespiration rate and temperature. Theplotted function (Q10 exponent of 2.2,normalized relative to respiration rateat 0ºC) is typical for microbial respira-tion in marine sediments (Robador etal. 2009; Stanley 2010). B) Relationshipbetween mean annual primary produc-tion (SeaWIFS data product forchlorophyll a concentration, units ofmg/m3) and mean annual sea surfacetemperature (MODISA data product)for equal-area grid cells in the globalocean for year 2010. There areapproximately 5.4 million observationsplotted. For context, average SST inthe MODISA dataset shown here is16ºC. Dotted line is an ordinary least-squares regression – no substantialrelationship between temperature andproductivity is apparent in the geodet-ic data. C) Temperature dependenceon O2 solubility from Henry’s law con-stant. Units are mol·L-1·atm-1. O2 solu-bility declines with increasing tempera-ture, but the expected change in sea-water O2 concentration for a givenchange in temperature is higher at lowstarting temperatures than at highstarting temperatures.

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consequence, rather than a cause, ofcarbon cycle perturbation. Nonethe-less, as long as a given set of changesin the fluid Earth carbon cycle affectstemperature, even as a corollary ofother drivers, a temperature-dependentthermodynamic feedback on organiccarbon burial can be expected.

This thermodynamic feedbackis positive, meaning it will tend toamplify the system response in bothatmospheric pCO2 (and consequentlyclimate) and in δ13C of marine carbon-ates. For example, it has been hypoth-esized that increased volcanic CO2 out-gassing at the Permian–Triassic bound-ary due to eruption of the SiberianTraps flood basalts produced a nega-tive C isotope excursion (Payne andKump 2007). In addition, however,warming associated with this CO2injection – supported by proxy obser-vations in Early Triassic paleoenviron-ments (Retallack 1999; Joachimski et al.2012) – would have increased micro-bial respiration rates and decreasedorganic carbon burial, leading to a larg-er negative δ13C excursion (and climateperturbation) than expected from thecarbon budget of the volcanic out-gassing alone. Similarly, the magni-tudes of positive δ13C excursionsattributed to external factors thatwould have also caused climate cooling(e.g. nutrient-driven organic carbonburial events (Saltzman 2005)) wouldhave been amplified by the tempera-ture-dependence of respiration.

The increase in respirationrates with temperature is clear in sign,but it is important to consider theeffect strength. A useful approach toevaluate the effect of a particular feed-back is to consider a simple referencesystem, and then estimate the systemgain as the amount of amplification ofthe response due to the inclusion offeedback (Roe 2009). The simplestdescription of the geological carboncycle is conveyed by classic steady-stateisotope mass balance formulations thatdescribe the δ13C values of carbonateand organic carbon as a function ofthe fraction of total carbon buried asorganic carbon over a given interval oftime (Summons and Hayes 1992;Kump and Arthur 1999). Formally,this system is not temperature sensitiveuntil the thermodynamic feedback ofStanley (2010) is included. Stanley

(2010) appreciated that the bigger thetemperature change, the larger theeffect on the carbon cycle (due toexponential differences in remineraliza-tion rates), but the nonlinearitybetween temperature and respirationrate means there is another importantadditional element that bears on thegain – the initial temperature boundarycondition. This feedback is expectedto be non-linear. Because global sea-water temperatures have almost cer-tainly varied significantly over Phanero-zoic time, it is important to estimatethe impact this feedback might havehad on the global carbon cycle as afunction of both amount of tempera-ture change and initial temperature.

We begin with a simple steady-state isotope mass balance frameworkand assume that the long-term, steady-state remineralization rate of organiccarbon (Fremin) is tightly controlled byexternal factors [over long timescales(> 106yr) the amount of remineraliza-tion is closely tied to productionbecause of negative feedbacks in O2and nutrient cycles (Lasaga and Ohmo-to 2002)] and is independent of tem-perature. This assumption is support-ed by the observation that baseline val-ues of δ13Ccarb are essentially invariantover Phanerozoic time (Saltzman andThomas 2012) despite well-document-ed changes to background global cli-mate and surface temperatures overthis interval (Frakes et al. 1992). Incontrast, short-term (~105-106 yr) tem-perature changes will impact marinerespiration rates (and δ13C) because ofthe observed thermodynamic (e.g. –‘Q10’) dependence on the microbialmetabolisms responsible for organiccarbon remineralization (Robador et al.2009; Stanley 2010). The exponent(i.e. strength) of this relationship variesamong environments, but a typicalopen-marine value is ~2.2 (Fig. 2A;Robador et al. 2009; Stanley 2010).Thus, the change in organic carbonremineralization flux (ΔFremin) is expect-ed to approximately double for a 10°Cincrease in temperature. It is alsoimportant to note that the absolute dif-ferences in respiration rates due to achange in temperature depend stronglyon initial temperature (Fig. 2A).

In principle, and at organismalscales, the same thermodynamic effectsthat cause heterotrophs to respire

faster at higher temperature also applyto primary producers. That is, holdingall other factors constant, a givenchange in temperature should influencethe metabolic rates and populationgrowth rates of both heterotrophs andautotrophs (Gillooly et al. 2001; Savageet al. 2004). If both productivity andmicrobial respiration had similar posi-tive exponential relationships to ambi-ent temperature, there would be no neteffect on fractional organic carbonburial. However, over even shorttimescales productivity is limited bylight and nutrients (and grazing,phages, etc.). To quantify the relation-ship between temperature and produc-tivity in the modern ocean we acquiredgeodetic data products for the year2010 from the MODIS Aqua (sea sur-face temperature) and SeaWIFS (seasurface chlorophyll a concentration)missions, and coupled them to thesame grid matrix using the softwareSeaDAS (http://seadas.gsfc.nasa.gov/)so they could be readily compared.The global observations show no sig-nificant relationship between primaryproduction (as measured by chla con-centration) and sea surface temperature(Fig. 2B) – if anything, the data sup-port a slight negative relationship asmore primary productivity is tied toupwelling of cold, nutrient-rich waters(chla = −0.0218T + 0.7964). Overall,while temperature changes will stronglyimpact rates of remineralization, pri-mary productivity is expected to oper-ate largely independent of temperature(or may even decline at higher temper-atures due to reduced upwelling, e.g.Behrenfeld et al. 2006). Consequently,there is no strong relationship betweenmean surface temperature and meanannual productivity (Fprod) in the mod-ern ocean (Fig. 2B), and no consensuson the expected relationship, if any,between changes in climate andchanges in primary productivity(Taucher and Oschlies 2011).

If we assume that Fprod doesnot vary as a strong function of tem-perature, it follows that the proportionof gross primary production that isremineralized (frem) is expected toincrease with temperature. The magni-tude of the expected change in frem fora given change in temperature can beestimated by:

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(Eq. 1)

Where T1 represents the initial meantemperature, T2 the mean temperaturefollowing a climate change, and Q10represents the mean relative change inglobal microbial respiration rate for a10°C change in temperature. Here, weassume that remineralization scales as asimple function of global mean tem-perature, though the global remineral-ization flux may depend not just onthe mean but also on the shape of theprobability distribution function ofglobal temperatures. Under a steady-state model with invariant Fprod, achange in relative remineralization ratemust be offset by an equal but oppo-site change in organic carbon burial:

(Eq. 2)

The corresponding change in the rela-tive organic carbon burial flux (forg) willshift the stable isotopic composition ofthe marine dissolved inorganic carbonreservoir according to the followingexpression:

(Eq. 3)

Where ε represents the fractionationfactor (due to biological kinetic isotopeeffects) between coeval dissolved inor-ganic carbon and organic carbon in theoceans. The isotopic composition ofmarine DIC, in turn, is recorded inmarine limestones as δ13Ccarb. Thus,using the above formulation, it is pos-sible to relate the sign and magnitudeof an isotope excursion in δ13Ccarb to atemperature-driven change in the effi-ciency of organic carbon respiration.

Critically, because the relation-ship between Frem and temperature isexponential rather than linear, the mag-nitude of δ13Ccarb excursion expectedfor a given change in mean tempera-ture will also change as a function ofinitial mean temperature (T1). Forexample, cooling from a mean temper-ature of 25° to 20°C would be expect-ed to generate a larger positive δ13Ccarbexcursion than cooling from 20° to

15°C, which in turn would be expectedto generate a larger positive δ13Ccarbexcursion than cooling from 15° to10°C.

Figure 3 quantifies the non-linear system gain from including athermodynamic respiration rate-organ-ic carbon burial feedback, in a classicgeological carbon cycle isotope massbalance framework. These relation-ships illustrate the sign and magnitudeof δ13Ccarb excursion expected for dif-ferent combinations of initial tempera-ture and change in temperature, assum-ing the same value for ε, here set at thePhanerozoic average of –29‰ (Hayeset al. 1999). Note that the availablefeedback strength estimates are poten-tially large (several ‰) for plausibleranges of historical Earth system cli-mate changes. An additional interest-ing consequence of the exponentialrelationship between temperature andrespiration rate is that the magnitudeof negative δ13C excursion, expectedfrom a given amount of warming,

exceeds the magnitude of the positiveexcursion expected from an equalamount of cooling.

DISCUSSION AND CONCLUSIONSThere are many aspects of physical,chemical, and biological oceanographicsystems that exhibit temperaturedependence – some of these may drivepositive or negative feedbacks onorganic carbon remineralization ratethat would act to amplify or damp thesystem response in addition to thefeedback discussed above. One suchfeedback that is immediately apparentis the inverse relationship between O2solubility (and concentration in seawa-ter) and water temperature (Emersonand Hedges 2008; Fig. 2C). Becauseorganic carbon preservation is stronglyaffected by oxygen availability (Hart-nett et al. 1998; Hedges et al. 1999),increased O2 concentrations at lowerseawater temperatures could act as anegative feedback to counter theexpected decrease in remineralization

Figure 3. Expected sign and magnitude of marine carbonate δ13C excursions as afunction of starting temperature and change in temperature for a steady-state iso-tope mass balance carbon cycle model with a temperature-dependent organic car-bon burial feedback. Note the strong effect of the initial boundary condition aswell as the asymmetry of isopleths with respect to sign of temperature change:because of the exponential relationship between temperature and respiration rate,the magnitude of the negative δ13C excursion expected from a given amount ofwarming exceeds the magnitude of the positive excursion expected from an equalamount of cooling.

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rate due to reduced microbial metabol-ic activity. Although the potentialimportance of this negative feedback isdifficult to evaluate rigorously, wepoint out that the inverse relationshipbetween O2 solubility and water tem-perature also has an exponential form(Fig. 2C) and will be differentially sen-sitive to an initial temperature bound-ary condition (i.e. dO2/dT is not a con-stant). Whereas relative changes inmicrobial carbon remineralization for agiven change in temperature areexpected to increase at higher baselinetemperatures, relative changes in O2solubility decrease at higher baselinetemperatures. Thus, to the extent thata change in δ13CDIC reflects the neteffects of changes in microbial meta-bolic activity and changes in oxygenavailability on Frem, the magnitude ofthese changes is still expected todepend strongly on initial temperature.

Temperature changes couldalso influence the delivery of O2 tobottom waters and sediments viachanges in ocean circulation, but for agiven change in temperature it is, atpresent, difficult to predict even thesign, much less the magnitude, ofexpected changes in the ocean mixingprocesses (IPCC 2007). Furthermore,changes in the mean temperature ofthe global oceans would not be feltequally everywhere – the magnitude ofδ13CDIC change expected would likelydepend disproportionately on coastaltemperature changes, and changes inseasonality in the high-productivityregions where most organic carbonburial and remineralization takes place.Because most of organic carbon burialtakes place on continental shelves(Reimers et al. 1992), especially indeltaic systems (McKee et al. 2004),and organic carbon remineralization isconcentrated in the upper 1 km of theocean (Jørgensen and Kasten 2006),δ13CDIC changes will be especially sensi-tive to temperature changes in shallowocean basins.

Though the calculationsexplored above do not represent acomprehensive biogeochemical view ofthe geological carbon cycle, theapproach can be used to predict thesign and magnitude of the δ13Ccarbexcursion accompanying a rapidchange in mean ocean temperature, ifT1, T2, Q10, and ε are known. And the

expectations can be compared to geo-logical observations of two well-knowncarbon isotopic excursions in thePhanerozoic record—both of whichare known to be associated with transi-tions from relatively warm conditionsto glacial ’icehouse’ states but are sepa-rated by more than 400 million years:the Paleogene Eocene–Oligoceneboundary excursion and the LateOrdovician Hirnantian excursion.

As noted above, Stanley(2010) singled out the Eocene–Oligocene event as puzzling becausethe climate cooling produced only arelatively small ~1‰ positive δ13Ccarbexcursion. The Mg/Ca data fromplanktic foraminifera suggest that trop-ical surface waters cooled by about2.5°C across this boundary, from~30.5° to 28°C. Although we havesome constraints on tropic SSTs fromproxy data, we do not know the distri-bution of temperatures in the upperkilometre of the oceans with any cer-tainty. Consequently, we make the sim-plifying assumption (based on the dis-tribution of temperatures in the 2010MODISA dataset) that the differencebetween the mean temperature oftropical surface waters and the meantemperature of the upper 1 km of theocean was the same in theEocene–Oligocene as it is today –about 15°C (Robador et al. 2009;Locarnini et al. 2010). Using a typicalearly Cenozoic ε value of 29‰ (Hayeset al. 1999), a mean Q10 exponent of2.2, and assuming a change in meantemperature from 15.5° to 13°C, ourmodel predicts a positive δ13Ccarb excur-sion of nearly 1‰ (Fig. 4). For theHirnantian glacial maximum, we makethe same calculation with a somewhathigher initial mean temperature for theupper oceans of 20°C. This assumesthe same 15°C difference betweentropical surface temperatures and themean temperature of the upper 1 kmof the oceans as above, and a meantropical sea surface temperature of35°C based on clumped isotope meas-urements of well-preserved, shallow-marine carbonates (Finnegan et al.2011). Using ε of 29‰ (a value typicalfor this interval (Hayes et al. 1999;Jones et al. 2011)), the observed 5°Ccooling predicts an excursion ofroughly 3‰ (Fig. 4). This estimate isslightly less than the observed excur-

sion, which varies from 4–6‰ globally(Brenchley et al. 2003; Jones et al.2011), but implies that reduced organiccarbon remineralization driven by cool-ing can plausibly account for a sub-stantial portion of this large positiveexcursion. This predicted value alsosubstantially exceeds the ~1.7‰ excur-sion that would be predicted for a sim-ilar drop in temperature using the LateEocene mean temperature estimate(Fig. 4).

Although we only have suffi-cient data to rigorously consider twoexamples from opposite ends of thePhanerozoic Eon, a temperature-dependent organic carbon burial mech-anism may help to explain the relativemagnitudes of other conspicuous δ13Cexcursions observed in the Phanero-zoic record. It is notable, for example,that some of the largest post-Cambri-an carbon isotope excursions – bothpositive and negative –occur during theEarly Triassic (Payne et al. 2004), aninterval that appears to have beenexceptionally warm (Retallack 1999).This feedback could also help toexplain the overall decline in the aver-age magnitude of δ13C excursions overPhanerozoic time, if the average tem-perature of organic carbon burial envi-ronments also declined over the sameinterval. Several lines of reasoningsuggest this was the case.

The mean δ18O of benthic cal-cifiers has increased by more than sev-eral permil since Cambrian time(Prokoph et al. 2008), with similartrends observed in marine cherts(Karhu and Epstein 1986), and phos-phates (Luz et al. 1984; Karhu andEpstein 1986; Trotter et al. 2008).This pattern implies either a substantialcooling of the seawater temperaturesor a systematic increase in the δ18O ofseawater through exchange with ocean-ic crust or some other mechanism (Jaf-frés et al. 2007). Robust interpretationof this trend remains controversial (e.g.Giles 2012), but recent new analyticalapproaches using the clumped isotopeproxy applied to Ordovician–Siluriancarbonates (Came et al. 2007; Finneganet al. 2011) reconstruct warm tropicalocean temperatures (e.g. 30° – 39°C)and do not support the hypothesis ofexceptionally light early Paleozoic sea-water δ18O values. Although theseclumped isotope studies provide broad

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support for the hypothesis of long-term Phanerozoic climate cooling(interposed by episodes of glaciation),coverage of the sedimentary record iscurrently limited and work is ongoingto better understand how this newproxy records climate information overgeological time in a regime of ever-present carbonate diagenesis.

Another line of logic also sug-gests that a general decline in the aver-age temperature of organic carbonburial environments occurred – even inthe hypothetical case that average sur-face temperatures have been constantthroughout the Phanerozoic. This is

due to the changing distribution ofcontinents through time and to secularchanges in the nature and environ-ments of organic carbon burial (e.g.Scotese 2001; Peters 2006). Mostorganic carbon burial takes place oncontinental margins, and consequentlythe meridional distribution of conti-nental shelf and slope area captures afirst-order control on global mean car-bon remineralization rates. Given thegeneral movement of continents fromtropical to temperate latitudes follow-ing the Triassic breakup of Pangea(Scotese 2001), it is reasonable to con-clude that most carbon burial today

takes place under cooler environmentaltemperatures than it did during muchof Paleozoic time.

We emphasize the utility ofthinking about this temperature-dependent organic carbon burial mech-anism as an internal feedback operatingin the carbon cycle that may amplifythe system response (as observed bythe magnitude of δ13C excursions) to agiven perturbation. What we find par-ticularly surprising is that the strengthof this feedback could be quite large.Our estimates of effect strength revealthat this feedback may play a firstorder role in carbon isotope excur-sions, and explain a substantial portion(up to several permil) of the magni-tude of a given excursion. While theseestimates may not remain as largewhen considered more comprehensive-ly in more complex biogeochemicalmodels that include other (positive andnegative) feedbacks (e.g. Ridgwell andZeebe 2005), we would expect theeffect to remain important and ever-present. More specifically, the depend-ence of this thermodynamic organiccarbon burial feedback on the initialtemperature boundary condition raisesthe possibility that the decreasing mag-nitude of carbon isotope excursionsover time may be due, at least in part,to long-term Phanerozoic climate andgeodynamic trends.

Finally, reflecting on carbonisotope trends through all of Earthhistory, the volatile Neoproterozoicrecord (Knoll et al. 1986; Halverson etal. 2005) highlights a yawning dividebetween the ways in which Phanero-zoic climate and the carbon cycle inter-acted and that of earlier Earth history.Although Proterozoic paleotempera-ture proxy estimates do not yet existthat allow direct comparisons to bedrawn, it appears clear that theobserved sign is opposite of expected– Neoproterozoic glaciations coincidewith large negative (Hoffman et al.1998; Rose et al. 2012), rather thanpositive carbon isotope excursions. Tothe degree that the temperature-dependent feedback discussed here iscorrect, it must have been overriddenby stronger drivers during much ofNeoproterozoic time (Schrag et al.2002; Tziperman et al. 2011). Uncov-ering the nature of these differenceswill be critical to understanding the

Figure 4. Two functions depict the expected relationship between amount ofcooling and change in δ13C for the terminal Eocene (black line) and Late Ordovi-cian (grey line) glaciations, respectively. These calculations were made usingboundary conditions based on tropical sea surface temperature estimates from(Lear et al. 2008) and (Finnegan et al. 2011), respectively, and assuming a constant15°C difference between tropical SST and mean temperature and using a Q10 of2.2. Points and error bars represent actual estimated cooling and from the samesources and the magnitude of the accompanying δ13C excursion. Excursion magni-tudes from Saltzman and Thomas (2012) and Jones et al. (2011), respectively.

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behaviour and evolution of climateand the carbon cycle over long inter-vals of Earth history.

ACKNOWLEDGEMENTSWe wish to express our gratitude toPaul Hoffman who introduced us to,and greatly stimulated our interests in,paleoclimate and the history of thecarbon cycle during many late nights inCambridge, MA. We thank AndyThompson and Ian Eisenman forinsight into the complexities of pre-dicting ocean circulation changes as afunction of temperature. The observa-tions in Fig. 2B, collected and madeavailable by the MODIS and SeaWIFSmissions, were made possible, in part,by NASA. This work was supportedby Agouron Institute awards to WWFand DAF, Packard Fellowships toWWF and DAF, and a National Sci-ence Foundation (EAR-1053523)award to WWF.

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Received June 2012Accepted as revised September 2012