Abstract

The Cretaceous to early Paleogene (ca. 140–50 Ma) was characterized by a greenhouse baseline climate, driven by elevated concentrations of atmospheric CO2. Hypotheses for the elevated CO2 concentrations invoke an increase in volcanic CO2 production due to higher oceanic crust production rates, higher frequency of large igneous provinces, or increases in pelagic carbonate deposition, the last leading to enhanced carbonate subduction into the mantle source regions of arc volcanoes. However, these are not the only volcanic sources of CO2 during this time interval. We show here that ocean-continent subduction zones, manifested as a global chain of continental arc volcanoes, were as much as 200% longer in the Cretaceous and early Paleogene than in the late Paleogene to present, when a cooler climate prevailed. In particular, many of these continental arcs, unlike island arcs, intersected ancient continental platform carbonates stored on the continental upper plate. We show that the greater length of Cretaceous–Paleogene continental arcs, specifically carbonate-intersecting arcs, could have increased global production of CO2 by at least 3.7–5.5 times that of the present day. This magmatically driven crustal decarbonation flux of CO2 through continental arcs exceeds that delivered by Cretaceous oceanic crust production, and was sufficient to drive Cretaceous–Paleogene greenhouse conditions. Thus, carbonate-intersecting continental arc volcanoes likely played an important role in driving greenhouse conditions in the Cretaceous–Paleogene. If so, the waning of North American and Eurasian continental arcs in the Late Cretaceous to early Paleogene, followed by a fundamental shift in western Pacific subduction zones ca. 52 Ma to an island arc–dominated regime, would have been manifested as a decline in global volcanic CO2 production, prompting a return to an icehouse baseline in the Neogene. Our analysis leads us to speculate that long-term (>50 m.y.) greenhouse-icehouse oscillations may be linked to fluctuations between continental- and island arc–dominated states. These tectonic fluctuations may result from large-scale changes in the nature of subduction zones, changes we speculate may be tied to the assembly and dispersal of continents. Specifically, dispersal of continents may drive the leading edge of continents to override subduction zones, resulting in continental arc volcanism, whereas assembly of continents or closing of large ocean basins may be manifested as large-scale slab rollback, resulting in the development of intraoceanic volcanic arcs. We suggest that greenhouse-icehouse oscillations are a natural consequence of plate tectonics operating in the presence of continental masses, serving as a large capacitor of carbonates that can be episodically purged during global flare-ups in continental arcs. Importantly, if the global crustal carbonate reservoir has grown with time, as might be expected because platform carbonates on continents do not generally subduct, the greenhouse-driving potential of continental arcs would have been small during the Archean, but would have increased in the Neoproterozoic and Phanerozoic after a significant reservoir of crustal carbonates had formed in response to the evolution of life and the growth of continents.

INTRODUCTION

Earth’s surface temperature is controlled by the radiative energy balance of the atmosphere, which depends on insolation, albedo, and atmospheric composition, particularly the partial pressure of atmospheric CO2 (pCO2), a greenhouse gas (Kasting, 1993). Atmospheric pCO2 is governed by exchange of C with other reservoirs of the exogenic C cycle (ocean and biosphere) and endogenic C cycle (crust and mantle) (Berner et al., 1983; Royer et al., 2004). On time scales >0.5 m.y., the exogenic system can be considered a single entity, with a mass of C dictated by inputs and outputs. Volcanism and metamorphism release CO2, weathering produces HCO3, and deposition of organic matter and carbonate sequesters C (Berner, 1994; Kerrick, 2001; Ridgwell and Zeebe, 2005). The global cycling of C is completed on even longer time scales (>10 m.y.) when subduction of oceanic lithosphere transfers C into the deep Earth, and volcanic eruptions return this C to the atmosphere. Continental collisions also result in metamorphic decarbonation of limestones and in exposure and weathering of limestone and organic matter (Berner, 1994; Kerrick, 2001; Ridgwell and Zeebe, 2005). This is how the long-term C cycle is currently understood.

If long-term C sources and sinks were balanced, atmospheric pCO2, averaged over millions of years, would remain relatively constant, and so would Earth’s surface temperature, unless insolation changes. This has not been the case over Earth’s history (Royer et al., 2004; Veizer et al., 2000) (Fig. 1A). Earth’s surface temperature changed significantly from the warm baseline of the Cretaceous and early Paleogene (ca. 130–50 Ma), which was characterized by relatively high sea level and a general lack of ice sheets (Hallam, 1984, 1985; Haq et al., 1987; Jenkyns et al., 2004; Müller and Groves, 1993; Forster et al., 2007; Wilson and Norris, 2001), to the cooler baseline of the late Paleogene to present (ca. 34–0 Ma), which was marked by large, though variable, ice sheets (Figs. 1A, 1B) (Hallam, 1985; Raymo, 1994; Zachos et al., 2008). Atmospheric pCO2 is thought to have been 4–8 times higher during the Cretaceous and early Paleogene (1200–2400 ppm) than during the Holocene (∼300 ppm) (Fig. 1B); this suggests that the warm baseline was driven by greenhouse conditions (Bice et al., 2006; Hong and Lee, 2012; Pagani et al., 2005; Pearson and Palmer, 2000; Royer et al., 2004). Based on these examples, the cycling of C between the endogenic and exogenic systems has clearly changed over long time intervals: the question is why.

CURRENT VIEWS ON AND QUESTIONS ABOUT CRETACEOUS–PALEOGENE GREENHOUSE

We use the Cretaceous–Paleogene greenhouse interval to explore possible causes of long-term climate variability. The most popular explanation for elevated atmospheric pCO2 during this time interval centers on greater production of basaltic oceanic crust through faster mid-oceanic ridge spreading rates and/or increased frequency of large igneous provinces (LIPs) (Fig. 1C; Berner and Kothavala, 2001; Hong and Lee, 2012; Kidder and Worsley, 2010; Larson, 1991a; Müller et al., 2008). This view appears consistent with the generally low 87Sr/86Sr (Fig. 1D) and low Mg/Ca ratios of Cretaceous seawater (Fig. 1E), because faster spreading is thought to increase hydrothermal circulation rates through the ridge, which contributes unradiogenic Sr to seawater and consumes seawater Mg (Richter et al., 1992; Stanley and Hardie, 1998). Furthermore, at least two oceanic anoxic events (OAEs) during the Cretaceous have been attributed to eruption of LIPs and massive release of CO2 (Adams et al., 2010; Kerr, 1998; Sinton and Duncan, 1997; Tarduno et al., 1991; Turgeon and Creaser, 2008).

However, it is unresolved whether oceanic crust production rates were sufficient to increase atmospheric pCO2 by 4–8 times those of the present. To evaluate the contribution from oceanic crust production, we consider the following logic. The change in total C of the exogenic system (ocean + atmosphere) is given by 
graphic
where dCex/dt is the rate (t = time) of change in concentration of C in the exogenic system, j is the total CO2 input into the exogenic system (volcanic degassing + weathering of organic C and carbonate), and kex is the inverse response time for C sequestration from the exogenic system in the form of organic C and carbonate, and Cex is the concentration of C in the exogenic system. At the >1 m.y. time scales considered here, we can assume equilibrium between the ocean and the atmosphere. Then, following the assumption of Schrag et al. (2002) that the oceans are saturated in calcium carbonate, CaCO3, on long time scales, equilibrium, K, between CO2 in the atmosphere and ocean can be expressed as 
graphic
where [HCO3] is the bicarbonate ion in the ocean, [Ca2+] is the Ca2+ concentration in the ocean and pCO2 is atmospheric CO2 concentration. Because the dominant C species in the ocean is HCO3 (e.g., [HCO3] ∼ Cex) and the ocean-atmosphere system can be considered as steady state on time scales longer than 1/kex ∼ 1 m.y. (Dessert et al., 2001), Equation 2 and the steady-state form of Equation 1 combine to yield atmospheric pCO2 as a function of the input j of CO2 into the exogenic system: 
graphic

If the quantity in parentheses is constant, j scales approximately with the square root of atmospheric pCO2. Therefore, increasing pCO2 by 4–8 times requires a 2–2.8 times increase in CO2 input into the exogenic system. In all likelihood, the rate constant kex for CO2 withdrawal from the system would increase during greenhouse conditions (because weathering efficiency would increase in a greenhouse world), so this 2–2.8 times increase in CO2 output is a minimum.

What rates of oceanic crust production are needed to support such an increase in CO2 output? Outgassing from ridges scales linearly with spreading rate if mantle potential temperature and average mantle C content are not changing substantially over the time scales of interest, as seems likely (Marty and Tolstikhin, 1998; McGovern and Schubert, 1989). This is because melting at ridges is driven by passive decompression, and consequently CO2 flux through ridges scales as FVCm, where Cm is the concentration of C in the mantle, V is the half spreading rate, and F is the average melting degree (FV is the flux of oceanic crust production). Cm can be considered constant over 100 m.y. time scales. Perhaps more surprising is the observable fact that F, as inferred from oceanic crustal thickness and geochemical tracers, is independent of spreading rate V for all ridge segments except ultraslow spreading centers (Chen, 1992). However, the reasons for this are well understood on theoretical grounds: although the total amount of mantle passing through the melting regime beneath ridges will increase with increasing spreading, the fraction of such mantle that melts to form crust does not change (Langmuir et al., 1992). The only factor that can change F is a change in mantle potential temperature, but this effect is not large enough. For example, increasing present-day mantle potential temperature of ∼1350 °C (Courtier et al., 2007; Lee et al., 2009; Putirka, 2005) by 100 °C would increase F by at most ∼0.3 (see results of Katz et al., 2003). Lee et al. (2005) showed that mantle potential temperature beneath ridges may have been higher in the Cretaceous, but by no more than 100 °C (see fig. 9 in Lee et al., 2005). For these reasons, we expect magmatic flux of CO2 through ridges to scale close to linearly with spreading rate. Thus, a >2–2.8 times increase in CO2 input into the exogenic system, if driven solely by mid-oceanic ridge magmatism, requires an equivalent increase in global oceanic crust production rates.

Were oceanic crust production rates 2–2.8 times higher during the Cretaceous–Paleogene? Based on the areal distribution of seafloor ages, Rowley (2002) argued that global oceanic crust production rates were constant to within 20% over the past 200 m.y. In contrast, analyses of the same type of data by Larson (1991b) and Müller et al. (2008) suggest that global oceanic crust production rates may have been 1.5–1.75 times higher 50–140 m.y. ago compared to 0–50 m.y. ago. Demicco (2004) and Becker et al. (2009) suggested that 1.3–2 times higher rates in the Cretaceous are permitted by the seafloor-age distribution. All of these estimates of oceanic crust production are highly model dependent, so there is currently no consensus on how variable seafloor spreading was during the past 200 m.y. The highest estimated Cretaceous oceanic production rates may be sufficient to support Cretaceous greenhouse conditions, but the lower estimates are clearly insufficient. Until Cretaceous seafloor production rates can be better refined, additional sources of CO2 should be explored.

A second possibility is to include the contribution from LIPs. However, given the brief durations of LIPs (<2 m.y.) and the <1 m.y. response time of CO2 withdrawal from the exogenic system (Dessert et al., 2001), a LIP would have to erupt every ∼1 m.y. to sustain prolonged greenhouse conditions for the time interval of interest. While LIP frequency was certainly higher in the Cretaceous–Paleogene than the mid-Cenozoic, the frequencies are still far too low to sustain continuous and prolonged greenhouse conditions (Fig. 1C) (Müller et al., 2008).

A third scenario invokes an increase in pelagic carbonate deposition during the Cretaceous, possibly facilitated by the evolutionary rise of pelagic carbonate-secreting organisms in the early Mesozoic (Katz et al., 2004). Such a scenario would increase the delivery of carbonate to subduction zones, from which it follows that the output of CO2 through arc volcanoes would increase (Caldeira and Rampino, 1993; Edmond and Huh, 2003; Johnston et al., 2011). However, it is not obvious that enhanced sequestration of carbonate in oceanic crust would necessarily increase the total flux of CO2 out of arc volcanoes. Consider a modified form of Equation 1, which describes the change in C content of the exogenic system Cex: 
graphic
where dCex/dt is the rate of change of C in the exogenic system, Coc is the concentration of C in the subducted oceanic crust, kex,cc is the rate constant for sequestration of exogenic C into nonsubductable C on continental platforms, koc,ex is the rate constant describing the transfer of metamorphically decarbonated C from the subducted slab back to the exogenic system through arc volcanism, and kex,oc is the rate constant describing sequestration of exogenic C into oceanic crust in the form of carbonated sediments or veins in the oceanic crust. If we consider the case in which 100% of subducted carbonate is completely decarbonated and returned to the exogenic system through arc volcanoes, then the quantity in parentheses on the right side of Equation 4 equals zero, regardless of changes in the efficiency of pelagic carbonate deposition, e.g., if kex,cc varies. With 100% decarbonation of the subducted oceanic lithosphere, the steady-state concentration of C in the exogenic system, Cex, must then be given by j/kex,cc. It is clear that Cex must ultimately be driven by external forcings, i.e., j. The subduction factory, in the context of the foregoing hypothesis, is not an external forcing. Finally, metamorphic decarbonation in typical subducting slabs is likely to be far less than 100% efficient because the temperatures required for decarbonation increase with increasing pressure (Dasgupta and Hirschmann, 2010; Kerrick and Connolly, 2001; Tsuno and Dasgupta, 2012). For example, in Figure 2, it can be seen that decarbonation, even in the presence of silica and H2O, is unlikely to be extensive because typical slab temperatures are not hot enough. Thus, enhanced pelagic deposition of carbonates, in the absence of an external forcing of CO2, could even lead to a net decrease in exogenic C.

We can conclude that an increase in external forcing is necessary to drive elevated atmospheric pCO2 in the Cretaceous–Paleogene. While juvenile mantle inputs seem to be favored by the community, they may not, by themselves, be sufficient. One remaining possibility is to liberate CO2 from long-lived reservoirs of carbonate and organic C accumulated and stored on continents over the history of Earth. This can be done by weathering or by metamorphic decarbonation of continental carbonates. Metamorphic decarbonation of crustal carbonates in magma-poor orogenic belts, such as that caused by the collision of India with Eurasia, or in magmatically active extensional orogenies, such as in western North America, have been suggested to have driven warming pulses in the Eocene (Evans et al., 2008; Kerrick and Caldeira, 1994, 1998; Nesbitt et al., 1995), but as far as we know, the importance of continent-sourced carbonates has not been considered for the Cretaceous. We show next that metamorphic decarbonation of continental carbonates, facilitated by a greater length of continental arc volcanoes during the Cretaceous–early Paleogene, was capable of generating more CO2 than any of the mechanisms described here.

CONTINENTAL ARCS DOMINATED IN THE CRETACEOUS

Based on a compilation of geologic maps (see Appendix), continental arcs (e.g., Andean style volcanism) were longer in the Cretaceous to early Paleogene than in the mid-Cenozoic (Figs. 3A and 4). Cretaceous–Paleogene continental arc batholiths occur (1) along the entire North American Cordillera, from southern Alaska through western North America and into Mexico, (2) in the South American Cordillera, extending from Columbia to southern Chile, (3) along the southern margin of Eurasia extending from eastern Turkey through southern Tibet and into present-day southeast Asia, and (4) along the eastern part of Eurasia, extending from southern China through Korea, Japan, and eastern Siberia. The total length of these Cretaceous–early Paleogene continental arcs was ∼33,000 ± 3000 km, which is ∼63% of the present length of all subduction zones (52,000 km; Bird, 2003), or ∼200% greater than the length of present continental arcs, which include the Andes, Mexico, Cascades, Alaska, Kamchatka, and Sumatra (<16,500 km or ∼30% that of current subduction zones). The present-day configuration of subduction zones was largely defined ca. 50 Ma with the termination of continental arcs in southern and eastern Eurasia and in western North America (Dickinson, 1981; Jahn et al., 1990, 2000; Lapierre et al., 1997) and the initiation of widespread intraoceanic subduction and associated island arcs in the western Pacific, extending from Izu-Bonin-Mariana to Fiji and the Tonga-Kermadec convergent margins (Stern et al., 2012).

There are several implications. Continental arcs are built through continental crust, whereas island arcs (e.g., the modern Marianas and outer Aleutians) are built on oceanic lithosphere. Because carbonate production and preservation are favored in shallow waters, most of the global marine carbonate accumulation, at least until the Mesozoic, occurred over the relatively small area of continental shelves and slopes above continental or transitional crust rather than across the enormous expanse of the deep sea above oceanic crust (Wilkinson and Walker, 1989). Thus, continental arc magmas are more likely than island arc magmas to intersect sedimentary carbonates (Fig. 5). Because of the high temperatures (600–1200 °C) characteristic of magmas (Fig. 2), intrusion of magmas into carbonates can result in efficient decarbonation by contact metamorphism, assimilation, or metasomatic reaction with the magma. During decarbonation, every mole of carbonate (limestone or dolomite) that reacts with magma releases 1 mol of CO2 (CaCO3 + SiO2 = CaSiO3 + CO2). Interactions of crustal carbonates and magma, particularly hydrous magmas (Fig. 2B), can release significant amounts of CO2. Currently, this process is exemplified at Etna and Vesuvius in Italy, volcanoes that have erupted through thick sections of crustal carbonates (Tethyan carbonates). Evidence for extensive interaction of crustal carbonates and magma comes from the abundant skarn and endoskarn xenoliths in Etna and Vesuvius lavas (Fulignati et al., 2000; Iacono-Marziano et al., 2009) and from the anomalously 13C-enriched composition of fumarolic gases (Allard et al., 1991); the latter is consistent with a sedimentary carbonate source of CO2 rather than a mantle source. This could be inherited from carbonates in the upper continental plate or from subducted carbonates, but the presence of skarns and endoskarns requires interaction with carbonate wall rock in crustal magma chambers, indicating that at least some component of carbonate is derived from the upper plate.

To place carbonate-intersecting volcanoes like Etna and Vesuvius in context, we examine their contributions to the global CO2 output through volcanoes. Etna (crater summit and flank diffusion) puts out ∼6 × 1011 mol/yr based on SO2/CO2 measurements of degassed volatiles and SO2 fluxes (Allard et al., 1991). For comparison, the present-day global CO2 emission through subduction zones is ∼1.5–3.1 × 1012 mol/yr (Dasgupta and Hirschmann, 2010; Hilton et al., 2002; Marty and Tolstikhin, 1998; Sano and Williams, 1996), a flux primarily based on circum-Pacific volcanoes, which are mostly island arcs or juvenile continental arcs and where the amount of crustal carbonate is comparatively smaller. The present-day CO2 emission through mid-oceanic ridges is ∼1–5 × 1012 mol/yr (Dasgupta and Hirschmann, 2010; Marty and Tolstikhin, 1998; Sano and Williams, 1996). Subduction zones (excluding volcanoes, such as Etna and Vesuvius) and ridges collectively yield a CO2 output of ∼4–10 × 1012 mol/yr (Marty and Tolstikhin, 1998). Thus, Etna alone accounts for 10%–14% of the global CO2 output. Those volcanoes that produce the most CO2 thus appear to intersect thick sections of crustal carbonates, suggestive of a causal link between high CO2 production and magmatic emplacement into carbonate platforms. Examples of other high CO2-producing volcanoes, though less productive than Etna, include Merapi in Indonesia, where skarn xenoliths and zoned phenocrysts indicate magma interaction with carbonate wall rock in shallow magma chambers (Chadwick et al., 2007; Deegan et al., 2010; Toutain et al., 2009). Although more work is necessary to evaluate the relative contributions of crustal carbonate versus subducted carbonate to the flux of CO2 emitted by arc volcanoes, the examples indicate that crustal assimilation in magma chambers may play an important role when carbonates exist in the upper plate. We note that only 50 or so Etna-type volcanoes would increase the global CO2 volcanic output by a factor 3–7 relative to the present-day global output, more than enough to drive the Cretaceous greenhouse. In the following we consider a scenario in which the Cretaceous–early Paleogene was characterized by a global chain of carbonate-intersecting arc volcanoes.

EVIDENCE FOR WIDESPREAD MAGMATIC DECARBONATION OF UPPER PLATE CRUSTAL CARBONATES

We attempt to estimate the extent to which Cretaceous to early Paleogene continental arc volcanoes may have intersected crustal carbonates in the upper plate. For a conservative assessment of this possibility, we mapped the distribution of Phanerozoic carbonates deposited before the Cretaceous (Fig. 3B). Where batholiths were emplaced in Tibet, southeastern Asia, eastern China, and Korea, thick Paleozoic sedimentary sections containing carbonates covered much of the prebatholithic crust (Golonka et al., 2006). Mesozoic batholiths in the North American Cordillera appear to have intersected Proterozoic and Paleozoic sediments, as evidenced by abundant roof pendants in the region (Burnham, 1959; Kerrick, 1970; Lackey and Valley, 2004; Pickett and Saleeby, 1993). In some of these regions, sedimentary sections approach 10 km in thickness, and limestones and dolostones occur in >50% of the stratigraphy (Stevens and Greene, 1999). Few Paleozoic carbonates crop out in western South America, so the contribution of the Andean volcanism to decarbonation may have been small both in the past and the present. We estimate the length of continental arcs that may have intersected crustal carbonates to be ∼13,000 ± 2000 km, ∼25% of the total length of modern arcs. We use this estimate in the following discussion to predict how much CO2 may have been liberated.

We can further evaluate the areal extent of magmatic decarbonation by mapping the distribution of decarbonated residues, i.e., skarns. Skarns are seldom represented in large-scale geologic maps because of their heterogeneous nature; however, because they are often associated with strategic metal ores (W, Sn, Cu, and Zn) (Barton and Hanson, 1989), their distribution can be determined with some confidence. For example, scheelite (CaWO4) forms exclusively in carbonate skarns when the tungstate ion (WO42–) in the silicate magma replaces the carbonate ion (CO32–) in carbonate, liberating CO2 (Wan, 1987). The use of W alloys in armor-piercing warheads made W a strategic metal, particularly during World War II, so locations of scheelite deposits across North America are established (Albers, 1981; John and Bliss, 1993; Newberry and Einaudi, 1981; Sinclair, 1995; Werner et al., 1998). Not all skarns contain scheelite, and many skarns have likely been eroded, hence the distribution of scheelite is a minimum map extent of skarn formation. In Figures 6 and 7 we show the distribution of Cretaceous–Paleogene plutonic rocks in North America and the distribution of Cretaceous–early Paleogene skarns. The abundance of Cretaceous–Paleogene scheelite deposits throughout the length of contemporaneous batholiths in North America qualitatively suggests that extensive decarbonation of crustal carbonates may have taken place in these Cretaceous–early Paleogene continental arcs.

We can also shed insight on the vertical extent of skarn formation. Skarn formation in the Sierra Nevada has been documented at near-surface conditions and in the deep crust. For example, oxygen isotopic studies of Sierran skarn outcrops suggest pervasive infiltration of surface-derived waters, which implies formation conditions at <1 km depth, providing ideal conditions for decarbonation (D’Errico et al., 2012). Evidence for lower crustal decarbonation comes from scheelite-bearing skarns and calc-silicate metamorphic rocks in the southern Sierra Nevada, where intrusive rocks derived from paleodepths of 20 km have been exhumed (Ague and Brimhall, 1988; Pickett and Saleeby, 1993) (Fig. 7). These deep-seated skarns and/or endoskarns likely derive from the underthrusting of craton-derived sediments into the magmatic arc during Cretaceous time (DeCelles et al., 2009) (Fig. 5B). Magmatic assimilation of carbonated metasediments would be a likely source of mid-crustal decarbonation. In the Peninsular Ranges batholith (California), the protoliths of many enclaves in the plutons are crustal carbonates or carbonate-bearing sandstones, now manifested in a spectrum of lithologies including wollastonite-, diopside-, amphibole- or biotite-rich rocks (Fig. 8). In addition, pluton margins in contact with carbonate country rock are often metasomatized into endoskarns, often manifested in the form of plagioclase-quartz-pyroxene rocks representing the product of Ca and Mg metasomatism of the pluton bodies (Dyer et al., 2011) (Fig. 8).

Skarn formation associated with continental arc magmatism was thus pervasive throughout the North American Cordillera in both lateral and vertical extent during the Cretaceous and early Paleogene. The North American Cordillera represents only one-third of the Cretaceous–early Paleogene continental arcs that intersect crustal carbonates (see Figs. 3, 6, and 7). Existing global data sets suggest that this pattern of skarn formation also applies to Eurasia: some of the world’s largest scheelite deposits and associated skarns occur in Korea and southeast China, where late Mesozoic granitoids have intruded carbonates (Werner et al., 1998). Today, few arcs intersect carbonates, and as mentioned earlier, prebatholithic carbonates are few in the Andean arc. The likelihood of profound release of CO2 from magmatically induced decarbonation of crustal carbonates during the Cretaceous–early Paleogene was clearly high. We attempt to quantify this contribution of CO2 in the next section.

We emphasize that continental arc environments are more efficient at decarbonating crustal carbonates than continent-continent collisions (Kerrick and Caldeira, 1994) or decarbonating subducting lithosphere. This is because, in continental arcs, (1) magmatic intrusions advect heat into the crust, which elevates the geotherm (Fig. 2A), (2) temperatures of decarbonation are low at upper crustal pressures, and (3) high water/rock ratio hydrothermal circulation is more pronounced in the upper crust because of the abundance of meteoric waters as well as higher permeability. Decarbonation must be less efficient in continental collisions and in subducting slabs because the magmatic flux is small to negligible, the geotherm is depressed, and decarbonation temperatures are higher (due to higher pressures involved; Fig. 2A) (Huerta et al., 1999).

IMMEDIATE CONSEQUENCES OF A CONTINENTAL ARC–DRIVEN CLIMATE

There are several testable consequences of a greater length of continental arcs and a more expansive area of magma-carbonate interaction.

Enhanced CO2 Fluxes

The best way to estimate CO2 production from magmatically induced decarbonation of wall rock and assimilated sediments is to quantify the volume of carbonated sediments that have interacted with plutons and the extent to which decarbonation reactions have progressed. Although we showed that Cretaceous–Paleogene skarn deposits are ubiquitous, we are far from quantifying volumes and extents of decarbonation for each skarn deposit so that such data can be assimilated on a global scale. Nevertheless, we can obtain a crude estimate of the relative increase in CO2 production when carbonate-intersecting continental arcs are active. We do this by describing the volcanic input of CO2 (mass of CO2/time), j, as a perturbation to volcanic CO2 production in the late Cenozoic: 
graphic
where J is the global magmatic production rate of arc magmas, Co is the average concentration of CO2 in primitive undegassed arc magmas today, L is the additional fractional length of carbonate-intersecting continental arcs in the Cretaceous–Paleogene relative to the present, X is the mass fraction, relative to the mass of magma, of pure carbonate sediment assimilated into magmas or decarbonated in skarns, and Ccc is the concentration of CO2 in limestones and dolostones (44–48 wt%). The quantity JCo represents the present-day baseline of global CO2 output from arc volcanoes jo. Values for Co are highly uncertain because CO2 degasses readily at depth. An upper bound of 0.3–0.5 wt% for primary undegassed concentrations is indirectly inferred from the global CO2 fluxes from arc volcanoes, but estimates from melt inclusions are lower by an order of magnitude (Wallace, 2005). If we assume that global magmatic production of arc magmas remains constant and that the only change is in the proportion of island and carbonate-intersecting continental arcs, we can reexpress Equation 5 as a quantity relative to present-day volcanic inputs: 
graphic
where jo = JCo and accounts for the present-day global arc production of CO2.

We can calculate a minimum amount of CO2 produced during crustal decarbonation by constraining the amount of sedimentary carbonate directly assimilated into the magma. Oxygen isotopic compositions of evolved granitoid plutons in continental arcs are as high as ∼+10‰ relative to modern seawater, whereas juvenile mantle-derived magmas are +5‰ (Hill et al., 1986; Kistler et al., 2003; Mattey et al., 1994). Assuming that metasediments have oxygen isotopic compositions in excess of +20‰, it is not unreasonable for evolved granitoids to have assimilated >30% sediments or partial melts of sediments. Such estimates are consistent with those based on 87Sr/86Sr (Kistler et al., 1965). If carbonates make up, on average, one-third of platform sedimentary packages (Ronov, 1972), >10% assimilation of pure carbonate would be implied. Similar carbonate fractions are seen in the Paleozoic strata on the western margin of North America, through which the Cordilleran plutons intruded (Greene and Stevens, 2002; Stewart, 1972). Taking the additional length of carbonate-intersecting continental arcs L in the Cretaceous–Paleogene as ∼25% and maximum Co as 0.3–0.5 wt%, Equation 6 yields 3.1–4.6 times more production of CO2 than the present. This is a lower bound, because assuming a lower value for Co would increase the relative magnitude of Cretaceous–Paleogene CO2 production. In addition, skarn formation driven by hydrothermal fluid circulation in the contact aureole surrounding plutons would only add to these estimates (Kerrick and Caldeira, 1998; Nesbitt et al., 1995). In summary, if all of this CO2 escaped to the atmosphere, this would be more than sufficient to increase atmospheric pCO2 by the 4–8 times. If some of this CO2 is trapped in the crust or plutons in the form of secondary calcite veins, the estimated CO2 production would be lower. Carbonates, interpreted to be primary, are commonly observed in granitoid plutons, but at the <1% level (White et al., 2005). The pervasive occurrence is consistent with widespread fluxing of CO2 through continental arc magmas, but the trace levels suggest insignificant retention.

Enhanced Production of Marine Carbonate and Organic C

Higher atmospheric pCO2 in the Cretaceous to early Paleogene, if driven by enhanced CO2 production, should lead to enhanced outputs of carbon from the exogenic system, provided that burial efficiency keeps up with CO2 production. This is consistent with evidence for widespread deposition of carbonate platforms and extensive hydrocarbon source rocks during the Cretaceous and early Paleogene (Fig. 3A). Although higher pCO2 should decrease ocean pH on short (<10,000 yr) timescales, elevated CO2 emissions on long (>10,000 yr) timescales should enhance carbonate accumulation (Ridgwell and Zeebe, 2005; Leon-Rodriguez and Dickens, 2010). That is, if total carbon inputs to the exogenic carbon cycle are large, then the outputs from the exogenic system in the form of carbonates and organic C should be similarly large. Inputs and outputs balance on long time scales. This may explain the large quantities of limestones and black shales (and hydrocarbon source rocks) deposited during the Cretaceous and early Paleogene. It also follows that the carbonate compensation depth, i.e., the depth at which the sinking rate of carbonate equals the dissolution rate, may have deepened in the Cretaceous to early Paleogene, allowing more widespread deposition and preservation of carbonate in pelagic environments compared to the mid-Cenozoic to present. Pelagic carbonate deposition would be a consequence of higher inputs of CO2 into the exogenic system rather than the driver of higher inputs into the exogenic system.

Carbon Isotopic Composition of Volcanic CO2 Is Increased

Limestone and dolostone decarbonation would have enriched total volcanic inputs in 13C compared to typical mantle-derived CO2. This would cause an overall positive shift in the δ13C of the exogenic C cycle, consistent with the higher δ13C values for Cretaceous–early Paleogene marine carbonate relative to the late Cenozoic (Fig. 1D). For example, a 2‰–3‰ increase in seawater δ13C can be generated by a crustal carbonate decarbonation flux of CO2 equivalent to 50%–100% of the modern background emissions of CO2 into the atmosphere (Fig. 9; see Appendix for calculation details). For comparison, the same increase in seawater δ13C can be generated by increasing the proportion of organic C burial to 0.3–0.35 from 0.2 in the late Cenozoic or by decreasing the isotopic fractionation factor of C during organic C burial relative to seawater by 1%–1.5%. This calculation is more complicated if organic C, in addition to carbonate, is liberated as CO2 to the atmosphere during magma-sediment interaction. What is clear is that the C isotopic composition of inputs into the exogenic system is unlikely to be equal to canonical mantle.

Enhanced Ash Production

Continental arcs are also more explosive than island arc, ridge, and LIP volcanism due to their more evolved (andesite) and volatile-rich compositions. Continental arc volcanoes can thus spew fine ash into the high atmosphere, distributing it globally on time scales ranging from days to a few years (McCormick et al., 1995). On longer time scales (10–100 k.y.), physical and chemical weathering of the volcanic slopes would prolong the transport of particulates and solutes of volcanic origin into the ocean. This prediction is consistent with widespread Cretaceous bentonite deposits (altered ash) throughout western North America, as far as the modern Mississippi River, more than 2000 km east of the Cordilleran arc (Dawson, 2000; Elder, 1988; Nixon, 1973). It is interesting that during modern eruptions, marine phytoplankton have been shown to assimilate Fe and other metals from ash within a few days of eruption (Duggen et al., 2007), begging the question of whether organic C and ash deposition may have been closely associated in the Cretaceous to early Paleogene. It is possible that widespread ash deposition aided the diversification of diatoms and radiolarians, resulting in organic-rich chert deposits in some parts of the Pacific Ocean (Dumitrescu and Brassell, 2005) (Fig. 1F).

87Sr/86Sr of Seawater

We discuss here the possible impacts of a continental arc–driven world on seawater tracers, such as 87Sr/86Sr and Mg/Ca (Fig. 1). The 87Sr/86Sr of continental arc magmas should be intermediate between unradiogenic and radiogenic Sr, the former driven by juvenile magmatism and the latter controlled by assimilation of ancient continental crust components. Weathering of continental arcs might be expected to slightly increase the 87Sr/86Sr of seawater; this is seemingly inconsistent with the notably unradiogenic signature (0.7072) of Cretaceous–Paleogene seawater, and would seem to require enhanced oceanic crust production to compensate for this increase. However, the main orogenic belts during the Cretaceous–Paleogene were associated with continental arcs, whereas the orogenies in the mid-Cenozoic were characterized by continent-continent collisions (e.g., closing of the Tethys Ocean). Sr derived from weathering of collisional orogenies should be more radiogenic than that derived from continental arcs, and hence the Sr isotopic composition of the global continental weathering flux should have been lower in the Cretaceous–Paleogene than the mid-Cenozoic, simulating the effect of increased oceanic crust production.

We can quantify this effect by considering the following. Assuming steady state, seawater Sr isotopic composition is a mixture of continental-derived weathering flux and oceanic crust–derived hydrothermal flux: 
graphic
where Rsw, Rcc, and Roc are the 87Sr/86Sr of seawater, continental crust, and oceanic crust, and Xoc is the mass fraction of Sr in the ocean derived from hydrothermal alteration of oceanic crust. If Rsw = 0.707 for the Cretaceous and we adopt the values for continental and oceanic crust end members from Richter et al. (1992; Rcc = 0.711, Roc = 0.703), we find the hydrothermal fraction of Sr, Xoc, to be ∼0.48. Using the same end-member compositions for present-day Rsw of 0.7092, we find present-day Xoc to be 0.22, implying that the hydrothermal fraction of Sr decreased by 50% since the Cretaceous.

The Sr isotopic compositions of Cretaceous continental arcs are variable, but averages 0.706 due to the contributions from both juvenile and preexisting crust (Kistler and Peterman, 1973; Kistler et al., 2003; Lee et al., 2007). If continental weathering in the Cretaceous–Paleogene was dominated by continental arcs rather than continent-continent collisions, Rcc would be between 0.706 and 0.711. Considering Rcc of 0.710 and 0.709 would yield Xoc of 0.35 and 0.25, approaching the mid-Cenozoic values of Xoc calculated here. Thus, an equally plausible explanation for the unradiogenic nature of Cretaceous seawater is a change in the weathering substrate of continents rather than an increase in the proportions of hydrothermal to continental fluxes of Sr.

Mg/Ca of Seawater

Seawater Mg/Ca has traditionally been interpreted to reflect enhanced hydrothermal circulation of seawater through oceanic crust, resulting in the sequestering of Mg (Stanley and Hardie, 1998). One might be tempted to suggest that skarn formation could drive a fundamental change in Mg/Ca ratio of river waters and hence seawater. However, any carbonate-derived Ca and Mg would become locked in silicates during skarnification and would therefore not be simultaneously liberated with CO2 to the exogenic system. Subsequent weathering of skarns, if dominated by Ca skarns, could increase Ca input into the oceans, thereby decreasing seawater Mg/Ca. However, this effect would most certainly be diluted to some extent by the background weathering of igneous rocks and noncarbonate sedimentary rocks. We therefore do not expect to see any significant effects of enhanced skarn formation on seawater Mg/Ca.

However, it is important to note that continental arcs are often associated with dynamic subsidence of the continental plate, resulting in the development of extensive shallow seaways (Gurnis, 1992; L. Liu et al., 2008; S. Liu et al., 2011) (Fig. 3). Burns et al. (2000) suggested that times of low seawater Mg/Ca seem to have coincided with times of enhanced dolomite formation in shallow continental interior seaways. This begs the question of whether low seawater Mg/Ca in the Cretaceous–early Paleogene could have in part been driven by enhanced sequestration of Mg during diagenetic dolomite formation (Wilkinson and Algeo, 1989). At the very least, such a scenario should be considered in addition to the conventional view of hydrothermal sequestration in oceanic crust. Mg and Ca isotopic proxies of Cretaceous seawater might provide a tool for testing between these ideas.

FLUCTUATIONS BETWEEN CONTINENTAL AND ISLAND ARC STATES

A fundamental question is why continental arc magmatism was more prevalent during the Cretaceous and early Paleogene. This might be understood by considering different dynamics involved in ocean-ocean and ocean-continent subduction zones, the former generating island arcs and the latter generating continental arcs (Stern, 2002; Uyeda and Kanamori, 1979) (Fig. 10). In subduction zones where the upper plate responds passively to the rollback of the subducting slab, the upper plate extends, resulting in backarc rifting, the formation of a marginal basin, and the development of an island arc. If, however, the upper plate is actively pushed toward the trench or if slab rollback is impeded, the upper plate is placed into compression, closing the marginal basin to form a continental arc. Unlike backarc spreading behind intraoceanic subduction zones, the backarc regions in ocean-continent subduction zones are under compression, leading to large-scale folding, thrusting, and the development of large basins driven by dynamic subsidence (rather than by lithospheric thinning). This compressional regime is exemplified in the modern Andes and in the Cretaceous–early Paleogene North American Cordillera (DeCelles, 2004; DeCelles et al., 2009).

It is possible that global changes in the nature of subduction zones are consequences of the aggregation and dispersal of continents (Fig. 10). When continents are aggregated (e.g., Pangea), vertical heat loss is decreased through the stagnant continental lid and lateral heat loss is decreased by the presence of cold subducting oceanic lithosphere surrounding the continents (Gurnis, 1988; Lenardic et al., 2011). In contrast, the oceanic domain is overlain by a mobile thermal boundary layer, that is, the boundary layer subducts; this allows for more efficient convective heat loss from the oceanic domain (Lenardic et al., 2011). Numerical models show that with time, strong lateral temperature gradients between the oceanic and continental mantle domains might develop, giving rise to strong lateral pressure gradients, which eventually exceed a threshold beyond which large-scale mantle overturn between the two domains occurs (Lenardic et al., 2011). This disperses the continents and places the leading edges of the continents into compression, culminating in the development of continental arcs. We thus speculate that the global Cretaceous–early Paleogene flare-up of continental arc magmatism may have been driven by the diachronous break-up of Pangea. The ensuing mantle overturn predicted by the numerical models would be manifested in the form of broad upwellings, leading to decompression melting away from ridges. Such melting would be manifested in the form of effusive outpourings of basalt in intraplate environments. Thus, an evolution toward a continental arc-dominated regime should coincide with a higher frequency of LIPs, as appears to be the case for the Cretaceous to early Paleogene.

The Cretaceous–early Paleogene continental arc regime contrasts with the present-day Pacific Ocean system, where much of the western Pacific subduction zones are in rollback mode (Stegman et al., 2010; Uyeda and Kanamori, 1979). If such conditions reflect overall closing of an ocean basin, our numerical models (Lenardic et al., 2011) do not predict any large mantle overturns, so LIP frequency is expected to be low; this is the case for the mid-Cenozoic.

IMPLICATIONS FOR LONG-TERM CLIMATE VARIABILITY

Fluctuations between island arc– and continental arc–dominated states, if linked to the aggregation and dispersal of continents, must have operated for as long as plate tectonics have operated and continents have existed. Provided that significant crustal carbonate reservoirs have always existed, the CO2 content of the atmosphere should have fluctuated, on the ∼200 m.y. time scales of continent assembly and dispersal, between periods of C storage (island arc stage) and purging of CO2 (continental arc stage) (Fig. 10); icehouse baselines define the former and greenhouse baselines define the latter.

If the Cretaceous–early Paleogene greenhouse represents a continental arc–driven world, the icehouse conditions of the mid-Cenozoic to present result from a return of the Earth system to an island arc–dominated state, not from an increase in organic C and carbonate burial associated with chemical weathering of the Tibetan orogeny, as is commonly thought (Raymo and Ruddiman, 1992). Early Paleogene cooling may have thus been the result of the waning of continental arc magmatism in North America during the Late Cretaceous. This cooling may have been temporarily interrupted by a last spurt of CO2 production associated with an Eocene magmatic flare-up in western North America (Kerrick and Caldeira, 1998), possibly giving rise to the Early Eocene climatic optimum ca. 52 Ma. However, the overall trend in the Cenozoic appears to be that of cooling. Stern et al. (2012) showed that, ca. 52 Ma, new intraoceanic subduction zones were initiated over much of the western Pacific, including the Aleutians and a broad stretch of subduction zones extending from Izu-Bonin-Mariana to Fiji and Tonga-Kermadec. This resulted in the final shift from continental arcs to island arcs in the western Pacific and coincided with the termination of continental arc magmatism in southern Eurasia due to the collision of India and Eurasia. From this point on, the climate cooled considerably, culminating in the development of Antarctic ice sheets ca. 35–40 Ma (Zachos et al., 2008).

In summary, the extent to which continental arc and island arc fluctuations affected climate in Earth’s deep past depends on the size of the crustal carbonate reservoir. Without a significant crustal reservoir of carbonates, such tectonic fluctuations would operate without significant climatic effects. There are reasons to suspect that the size of the crustal carbonate reservoir has not been constant through time. Carbonates, being preferentially deposited on continental shelves and slopes, have a low probability of being subducted. This means that the mass of carbonates in the continents has likely grown with time, dictated in part by the evolution of life and the growth of the continents upon which the carbonates are deposited and stored (Ronov, 1972). It follows that long-lived tectonically driven fluctuations between greenhouse and icehouse states may be characteristics of Earth’s recent past (particularly after the Cambrian explosion of life) and perhaps absent early in Earth’s history.

We thank the Packard Foundation, the Miller Institute at the University of California–Berkeley, the Atmosphere and Ocean Research Institute of the University of Tokyo, and the National Science Foundation for indirect support. We thank D. Morton, A.W. Bally, B. Dyer, D. Scholl, D. Schrag, W. Leeman, D. Thomas, and F. Marcantonio for liberating discussions, and A. Maloof, R. Stern, K. Putirka, L. Kump, I. Dalziel, and K. Burke for constructive and critical reviews. We also thank D. Scholl and A. Fildani for help and encouragement.

APPENDIX. DISCUSSION OF METHODS AND RESULTS

Methods

Cretaceous–Paleogene paleogeography with regions of continental inundation and hydrocarbon source rocks in Figure 3 is adapted from Ulmishek and Klemme (1990). Continental arcs from this time were compiled from a number of references. Cretaceous–Paleogene batholiths occur along the (1) entire stretch of the North American Cordillera, extending from southern Alaska south through western North America and into Mexico (Barton, 1996; Coleman and Glazner, 1997; Kistler et al., 2003), (2) the South American Cordillera, extending from Columbia south to southern Chile (Kay et al., 2004), (3) the southern margin of Eurasia extending from eastern Turkey east through southern Tibet and into present-day southeastern Asia (Boztuğ et al., 2007; Golonka et al., 2006; Wen et al., 2008), and (4) the eastern part of Eurasia, extending from southern China (Li, 2000), north through Korea, Japan, and eastern Siberia (Akinin et al., 2009; Chough and Sohn, 2010; Kagami et al., 1992; Miller et al., 2002; Nakajima, 1996). The total length of continental arcs was estimated using the ruler tool in Google Earth. We also present the locations of Phanerozoic carbonates prior to the Cretaceous using the global carbonate map and paleogeographic study of Kiessling et al. (2003). This work was supplemented by that of Sengör and Natal’in (1996) and Meyerhoff et al. (1991) for China and Tibet, Golonka et al. (2006) for southeast Asia, Jaillard et al. (2000) and Ramos (2000) for South America, and for North America and Central America by Cook and Bally (1975).

The skarn database was based on the following sources. We first used literature compilations of scheelite, Sn-Mo, and Cu-Au skarns (Albers, 1981; John and Bliss, 1993; Newberry and Einaudi, 1981; Sinclair, 1995; Werner et al., 1998). These were amplified by extracting data on unpublished scheelite localities in the western United States using the U.S. Geological Survey Mineral Resources Data System (http://tin.er.usgs.gov/mrds/) and in British Columbia from the British Columbia Ministry of Energy mineral resources database MINFILE (http://minfile.gov.bc.ca/searchbasic.aspx). Additional skarn deposits from Alaska were taken from Newberry et al. (1997). Only Cretaceous and Paleogene skarns were selected for presenting in the text. Skarn ages correspond to the age of the magmatic intrusion, not to the age of the protolith or country rock. In some cases, pluton ages are described in the published literature. In many other cases, pluton ages are only shown in geologic maps. We correlated each skarn locality to the host pluton using geologic maps using OneGeology (www.onegeology.org), an online database of geologic maps based on the Geological Society of America Decade of North American Geology base map (Reed et al., 2005). The filtered skarn data were combined with the Geological Society of America base map in Arc GIS (geographic information system; http://www.esri.com) to produce Figure 7.

Strontium, carbon, and sulfur isotope data in Figure 1 are from the published database of Prokoph et al. (2008). Because we are interested in long-term (>10 m.y.) variations in these isotopic signatures of seawater, a running average based on 10 m.y. intervals was calculated.

Mass Balance Estimates

To estimate how magmatic decarbonation of crustal carbonates affects the C isotopic composition of the exogenic system and seawater, a simple mass balance is considered here. Under steady-state conditions, inputs and outputs must be balanced: 
graphic
Fvls and Fvw are the relative proportions of the CO2 inputs to the exogenic system from magmatically induced decarbonation of crustal carbonates (e.g., limestones and dolostones) in continental arcs and the background flux of CO2 from ridges, island arcs, and metamorphism and weathering of organic C and carbonates on continents, respectively. Forg and Fcarb are the relative proportions of CO2 outputs in the form of organic C burial and carbonate burial, the latter associated with the end product of chemical weathering of silicates. Rvls, Rvw, Rorg, and Rsw are the isotopic ratios of 13C/12C in crustal carbonates, mantle-derived CO2, organic C, and seawater, the latter of which we take, for simplicity, to be equivalent to carbonates precipitated from seawater. The isotopic ratio is related to δ13C notation as R = Rref (1 + δ/103), where Rref represents the ratio of a standard, such as Vienna Peedee belemnite (PDB). Equation A1 can be rewritten as 
graphic
where α = Rorg/Rsw represents the isotopic fractionation factor between organic C and seawater.
We now take the late Cenozoic as a background state in which magmatically driven decarbonation of crustal carbonates is negligible (Fvls ∼ 0) compared to the time interval of interest, the Cretaceous to early Paleogene. Mass balance, following the form of Equation A1, yields the relationship 
graphic
where the superscript zero is used to denote values corresponding to the reference state and Rvw is assumed to be constant with time so that we can isolate the influence of magmatic decarbonation in continental arcs. With the following definition, Ω ∼ Forg(α – 1) + 1, we can divide Equation A2 by Equation A3 to yield 
graphic
If the fractionation factor associated with organic C burial α and the proportion of organic C burial Forg to carbonate burial do not change, then Equation A4 reduces to the special case of 
graphic
which shows how seawater C isotopic composition, Rsw, changes when there is an added contribution of magmatic decarbonation of crustal carbonates, e.g., when Fvls > 0.
It is more useful to express Equations A4 and A5 in a form that allows us to explicitly estimate the mass flux of CO2 from magmatic decarbonation of crustal carbonates (jvls) relative to the background mass flux of CO2 (jvw). Recognizing that 
graphic
(a similar equation can be written for Fvls), Equations A4 and A5 can be modified algebraically to yield 
graphic
Equation A7 shows how much magmatic decarbonation of crustal carbonates is needed to change the C isotopic composition of seawater Rsw from a reference state Rosw. Note that Rvw is assumed constant and equal to the canonical C isotopic composition of the mantle given in delta notation as δ13CPDB = –5‰ (but this will change if the flux of CO2 from weathering of organic C and carbonate in continents is not –5‰), Rvls is the average C isotopic composition of crustal carbonates (0‰ to +1‰), and jvw is assumed to be a baseline flux of CO2 that does not change over the time interval of interest (because we are only assessing the influence of magmatic decarbonation of crustal carbonates). The latter assumption implies then that jvls/jvw represents the excess CO2 inputs into the atmosphere associated with magmatic decarbonation of crustal carbonates in continental arcs. If jvls/jvw = 0, i.e., there are no contributions from crustal carbonate decarbonation, then Equation A7 simplifies to 
graphic
Thus, if Forg and α remain constant and jvls is zero, Rsw does not vary with time, i.e., Rsw/Rosw = 1.

The sensitivity of Rsw to changes in Forg, α, and jvls/jvw can be assessed as follows. We take the present as a reference, so we assume that jvls/jvw is close to zero today. In delta notation, the C isotopic composition of seawater, α = 0.975, is equivalent to 0‰ (equivalent to a 13C/12C of 0.011237), Rvw is –5‰, and the isotopic composition of modern organic C is –25‰. This gives a modern fractionation factor between organic C and seawater of α = 0.975. Assuming that carbonate precipitation does not fractionate C isotopes, these values correspond to a modern organic C burial proportion of Foorg = 0.2, or 20% of the total deposition of C today is in the form of organic C and the remaining is in the form of carbonate. This is consistent with the analysis by Shackleton (1987).

Cretaceous–Paleogene seawater was characterized by C isotopic compositions that were 2‰–3‰ higher than the late Cenozoic. As can be seen from Figure 9, this can be achieved by increasing Forg from a late Cenozoic value of 0.2–0.3–0.35 or decreasing α by 1%–1.5%. It can also be seen that a magmatic decarbonation flux of 50%–100% of the Cenozoic CO2 flux into the exogenic system (equivalent to increasing the total inputs of C into the exogenic system by 1.5–2 times) can achieve the same effect. While it is difficult to separate the contributions of all these variables from the seawater carbon isotopic record, this analysis shows that the addition of crustal carbonate decarbonation can lead to a significant positive shift in the baseline C isotopic composition of the exogenic system.

Geotherms and Metamorphic Reactions

The steady-state geotherm in Figure 2A was calculated from the heat diffusion equation assuming a 25 °C surface temperature, and a fixed surface heat flux (80 mW/m2) for a two-layer model (35 km crust overlying mantle). The crust has a heat production of 1.7 μW/m3 and the mantle heat production is assumed to be zero. This geotherm is meant as a possible reference state for the lithosphere in an active arc setting. Metamorphic decarbonation curves as a function of pressure and temperature in Figure 2A were calculated thermodynamically using Theriak Domino software (de Capitani and Brown, 1987; de Capitani and Petrakakis, 2010). The reactions of interest are CaCO3 + SiO2 = CaSiO3 + CO2 and CaMg(CO3)2 + 2SiO2 = CaMgSi2O6 + 2CO2. Figure 2B shows isobaric decarbonation temperatures as a function of CO2 activity.