Carbon release from Large Igneous Province magmas estimated from trace element-gas correlations

Large Igneous Provinces (LIPs) facilitate massive transfers of CO 2 and other volatiles from the mantle to atmosphere, contributing to past global warming and environmental disruption. However, the scale and evolution of magmatic CO 2 ﬂuxes during these events remain uncertain due to the tendency of CO 2 to degas deep in magmatic systems. Here we estimate LIP CO 2 using an approach based on an observed correlation between gas CO 2 /S ratios and trace elements in volcanic rocks. We apply this method to a compilation of published geochemical data for tholeiitic LIP lavas and to a new major and trace element dataset for alkaline rocks from the Siberian Traps. Our results indicate that CO 2 /S and therefore CO 2 in tholeiitic and alkaline magma suites from LIPs span 1ś2 orders of magnitude, emphasizing that changing CO 2 concentrations can combine with magma ﬂux to drive strong variations in CO 2 release through the evolution of LIP magmatism.


INTRODUCTION
Major shifts in climate and the carbon cycle [e.g. Schaller et al. 2011;Joachimski et al. 2012;Armstrong McKay et al. 2014;Percival et al. 2017] coincide with emplacement of some but not all of the voluminous intraplate magmatic events known as Large Igneous Provinces (LIPs). Examples include the abrupt warming and negative carbon isotope excursion during thẽ 252 Ma end-Permian mass extinction coinciding with emplacement of the Siberian Traps [Joachimski et al. 2012;Chen et al. 2016;Burgess et al. 2017]; repeated jumps in atmospheric CO 2 during the~201.5 Ma end-Triassic mass extinction coinciding with emplacement of the Central Atlantic Magmatic Province [Schaller et al. 2011;Blackburn et al. 2013]; and the abrupt warming and carbon isotope excursion during the 56 Ma Paleocene-Eocene Thermal Maximum coinciding with emplacement of the North Atlantic Igneous Province [Gutjahr et al. 2017]. In contrast, emplacement of the~135 Ma Parana-Etendeka LIP, for example, seems to have resulted in negligible consequences for paleoclimate [Marks et al. 2014;Dodd et al. 2015].
Despite the growing evidence that some LIPs have strongly impacted Earth's carbon cycle, a decades-long controversy has focused on whether or not LIP magmas release sufficient quantities of carbon to explain the observed changes * bblack@eps.rutgers.edu [e.g. Caldeira and Rampino 1990;Self et al. 2006;Sobolev et al. 2011;Tobin et al. 2017;Black and Gibson 2019]. The assumption that mantle carbon release is insufficient to strongly perturb the ocean-atmosphere system has led to the alternative hypothesis that sedimentary carbon degassing drives observed carbon cycle changes [Svensen et al. 2004; Ganino and Arndt 2009]. A combination of primarily magmatic carbon and subordinate sedimentary or clathrate carbon has also been proposed to explain paleoclimate observations [Gutjahr et al. 2017;Black et al. 2018].
A key factor fueling this debate is the lack of direct constraints on the carbon budget of diverse LIP magmas, in contrast to growing data on sulfur and halogens [Thordarson and Self 1996;Self et al. 2008;Black et al. 2012;Callegaro et al. 2014;Marks et al. 2014]. Quantifying magmatic carbon (in all magmas, not just LIP magmas) is a major challenge because low carbon solubility at crustal depths [Dixon and Stolper 1995;Edmonds and Woods 2018] translates into a limited record of initial carbon content in volcanic or shallow intrusive rocks [Wallace et al. 2015]. As a result, magmatic CO 2 is in some sense a ghost, because it is largely lost from volcanic rocks at Earth's surface.
Tracking carbon in LIP magmas ( Figure 1) is thus critical to testing hypotheses for how solid Earth degassing relates to surface environmental change during key turning points in Earth's history. Droplets of melt trapped in crystals known as Figure 1: Schematic diagram illustrating the plumbing system feeding LIP magmatism and expected variations in Sr/Sm and CO 2 /S from the region of partial melting to the surface. Simplified from Black et al. [2021].
melt inclusions are protected from degassing and have been used to reconstruct melt CO 2 [Lowenstern 2001;Wallace et al. 2015;Capriolo et al. 2020], though it remains an open question how much decrepitation has shaped the observed distribution of melt inclusion CO 2 [Maclennan 2017]. Melt inclusion constraints on CO 2 from LIP magmas and selected hotspot volcanoes are summarized in Figure 2. While these data provide valuable snapshots of magmatic CO 2 , it is not possible to analyze melt inclusions spanning complete LIP stratigraphiesboth because of the care and time required for melt inclusion preparation and due to gaps in suitable samples. Furthermore, a large proportion of melts trapped in melt inclusions have degassed relative to primary melt CO 2 concentrations (Figure 2), and many LIP melt inclusion suites lack data for CO 2 in vapor bubbles, motivating the search for alternative methods to constrain primary CO 2 .
In this study, we use a new empirical approach that relies on an observed correlation between trace element ratios in volcanic rocks erupted at modern volcanoes and the cor-responding volcanic gas CO 2 /S ratios [Aiuppa et al. 2021]. This approach relates the potentially heterogeneous melting regimes that produce LIP magmas to the gas mixtures expected at the surface ( Figure 1). We apply this method to reconstruct the CO 2 budget of tholeiitic magmas from major Phanerozoic LIPs. We further apply the method to a new dataset with whole-rock major and trace element geochemistry from alkaline Siberian Traps dikes, lavas, and volcaniclastic rocks.

RATIONALE AND METHODOLOGY
This work builds on the empirical correlation between wholerock Sr/Sm and Sr/Nd ratios and gas CO 2 /S ratios described in Aiuppa et al. [2021]. This empirical correlation was initially based on gas measurements from a suite of twelve ocean island and continental rift volcanoes (Figure 3), and has subsequently been applied to the 2021 Fagradalsfjall eruption in Iceland [Halldórsson et al. 2022]. These correlations (Figure 3 and 4) imply that, although CO 2 and S become fractionated VOLC V NIC V 6(1): 129ś145. https://doi.org/10.30909/vol.06.01.129145 Figure 2: Summary of melt inclusion CO 2 data for LIP and selected hotspot magmas. The interquartile range is shown as a gray box, and all individual data points are plotted as white circles. Ontong Java data are from Jackson et al. [2015]. Siberian Traps data are from Black et al. [2014]. Data from Laki in IcelandÐoften considered as an analog for flood basalt eruptionsÐare from Hartley et al. [2014]. Data from Canary Islands are from Taracsák et al. [2019], and are shown here to illustrate the range of CO 2 in hotspot magmas, as Canary Island magmas are among the most CO 2 -rich known ocean island basalts. Raman CO 2 densimeters require instrument-specific calibration [Lamadrid et al. 2017], introducing additional uncertainty for Raman vapor bubble CO 2 estimates for the Laki and Canary Islands datasets shown here. Deccan Traps data without quantifying CO 2 in vapor bubbles are from Choudhary et al. [2019], and from earlier units including CO 2 in vapor bubbles from Hernandez Nava et al. [2021]. Data from the Deccan Traps were generated using the calibrated Raman at Virginia Tech [Hernandez Nava et al. 2021]. N = Number of melt inclusions analyzed.
during magmatic degassing owing to their dissimilar solubilities in magmas [Oppenheimer et al. 2014], the time-averaged magmatic gas CO 2 /S ratio at each volcano is representative of its mantle source characteristics. In other words, the trace element and volatile abundances in the source mantle exert a dominant control on magmatic trace element ratios and gas CO 2 /S [Aiuppa et al. 2021]. A prerequisite for surface gas CO 2 /S to be source-controlled is that magmas evolve and degas under dominantly closed-system conditions, and that both CO 2 and S degas efficiently. For example, extensive sulfide formation or suppressed sulfur degassing during submarine eruptions could alter how source-imposed CO 2 /S ratios translate to gas compositions. Closed-system degassing is a recurrent [Shinohara 2008] but limited condition in mafic volcanic systems [Edmonds 2008;Edmonds et al. 2022]. Modern open-vent systems deliver gases from depth-integrated degassing of magmatic plumbing systems [Edmonds et al. 2022], and thus the modern calibration dataset may capture systematic differences in pressure-dependent degassing of CO 2 and S as well as ratios in primitive melts. Our aim in this work is to cautiously extend the observed correlation between whole-rock Sr/Sm and Sr/Nd ratios and gas CO 2 /S at modern volcanoes to estimate initial CO 2 /S and CO 2 in LIP magmas based on new and published whole-rock trace element data. Prior to doing so, we discuss the rationale for applying this empirical relationship from modern volcanoes to investigate ancient LIP magmas.
While ocean island and continental rift magmas differ from LIP magmas, they are also close cousins in several key respects. For example, LIPs and hotspots have been proposed Figure 3: Scatter plot of whole-rock Sr/Sm ratios vs. gas CO 2 /S ratios for twelve modern tholeiitic/alkaline volcanoes for which gas information is available [Aiuppa et al. 2021]. The best-fit regression line to the modern volcano dataset (equations and regression coefficients; equation in the figure) is used to estimate CO 2 /S ratios for individual LIP whole-rock samples based on their measured Sr/Sm ratio (data from Supplementary Material 2). The composition of the Depleted MORB Mantle (DMM) is from Workman and Hart [2005]. The MORB field is defined from compositions of MORB melt inclusions [Saal et al. 2002;Le Voyer et al. 2017] and glasses [Michael and Graham 2015;Le Voyer et al. 2019].
to originate from the heads and tails of mantle plumes, respectively [Richards et al. 1989]. In spite of the extreme compositional diversity spanned by LIP rocks as a whole [Ernst 2014], most tholeiitic LIP magmas have chemical and isotopic signatures [Hawkesworth and Scherstén 2007;Zhang et al. 2008] that overlap the compositional array of modern mid-ocean ridge and ocean island basalts [Pearce 2008], implying they originated from (similar degrees of) melting of a similar suite of mantle sources [Hofmann 2007]. Similarly, alkaline LIP magmas are most suitably approximated by the alkaline mafic to ultramafic rocks that are presently erupted in both intraplate contexts and (especially) during incipient continental rifting (e.g. in the southeastern and western branches of the East African Rift [Foley et al. 2012]), and they are thus likely to have formed by low degrees of melting of similarly fertile/enriched mantle sources [Ernst 2014]. Thanks to these similarities, modern ocean island and rift volcanoes and basaltic fissure eruptions have been used as potential analogs for LIP volcanism and gas emissions [Olmez et al. 1986;Self et al. 2006;Saunders 2016;Black and Gibson 2019]. The general agreement between the trace element systematics of LIP magmas and modern ocean island and rift magmas is demonstrated in Figure 4, and supports the overall relevance of tholeiitic to alkaline mafic rocks erupted by today's intraplate ocean islands (e.g. Hawai ' i), hot-spot related mid-ocean ridges (e.g. Iceland) and continental rifts (e.g. the East African Rift) as modern geochemical analogues for Phanerozoic LIP rocks.
Beyond the observed empirical correlation [Aiuppa et al. 2021], the conceptual basis for applying Sr/Sm and Sr/Nd as proxies for gas CO 2 /S ratios is the hypothesis that CO 2 enrichment of mantle sources is dominantly shaped by metasomatism involving carbonatitic to carbonated silicate melts that form by incipient melting of the deep upper mantle [Dasgupta 2013; O'Reilly and Griffin 2014; Sun and Dasgupta 2019; Aiuppa et al. 2021]. Sr is high in such melts, and is therefore a sensitive tracer of variations in mantle CO 2 related to metasomatism. Sr, Sm, and Nd have relatively similar behavior during mantle melting- Workman and Hart [2005] report bulk partition coefficients of Sr = 0.025, Nd = 0.031, and Sm = 0.045. Therefore Sr/Sm and Sr/Nd are poorly sensitive to melting degree fractions and crystal fractionation (provided calcic feldspar fractionation is minimal) [Aiuppa et al. 2021]. Importantly, this approach will not capture heterogeneity in mantle CO 2 that is not due to mantle metasomatism. Therefore, if LIPs are sourced from mantle plumes that tap distinct deep mantle reservoirs [Jackson and Carlson 2011], additional data from melt inclusions and other approaches are also required to assess heterogeneity in volatile systematics from such sources.
In addition to this published data, we include new major and trace element data from thirty-five alkaline lavas, dikes, and sills from the Maymecha Kotuy region of the Siberian Traps [described further in Fedorenko et al. 2000]. These samples include volcaniclastic rocks and lavas from the Pravoboyarsky and Aryzhangsky suites, which are thought to be among the earliest erupted products of Siberian Traps volcanism, with a U-Pb age of 252.24 ± 0.12 Ma from two perovskite bearing samples [Burgess and Bowring 2015]. They also include late-erupted alkaline lavas and intrusive rocks from the Delkansky suite and the Guli alkaline-ultramafic province. Major and trace element data from Siberian Traps alkaline rocks (Supplementary Material 3) were collected at Activation Laboratories. Major and trace element data were collected via fusion inductively coupled plasma mass spectrometry. Repeat analyses of standards and unknowns are provided in a separate tab in Supplementary Material 3. Based on replicate analyses of standards and unknowns, typical analytical uncertainties for major elements are typically a few percent, and for trace elements are <5-10 %.
For each sample with available trace-element information, we calculated the Sr/Sm and Sr/Nd ratio. The Sr/Sm and Sr/Nd ratios are then used to infer the corresponding gas (CO 2 /S) ratios using the best-fit equations for the modern volcano population [Aiuppa et al. 2021]: The suite of twelve modern alkaline/tholeiitic ocean island and continental rift volcanoes underlying these calibration equations (Equation 1 and 2) are thought to have formed from variable (4 to 18 %) degrees of melting of a peridotitic mantle in the 1.8-4.6 GPa pressure range [Aiuppa et al. 2021]. Estimated melting fractions for LIPs are similar overall to our calibration suite, but with alkaline magmas resulting from a few percent melting [Gibson et al. 2006;Black et al. 2021] whereas tholeiitic magmas are thought to originate from higher degrees of melting (typically in the 15-30 % range) [Herzberg and Gazel 2009], likely reflecting a shallower mantle source (melting depths for most LIPs are estimated at 50-100 km [White and McKenzie 1995]).
For both the tholeiitic and alkaline counterparts of each LIP, we calculate the median CO 2 /S ratios (Table 1). Ultimately, these are converted into estimated parental (un-degassed) melt CO 2 contents (Table 1) by scaling to the inferred parental melt S contents for each LIP. We use melt inclusion measurements as compiled in Black et al. [2021] and Supplementary Material 4 to estimate initial sulfur. For our estimates of CO 2 we opt to use the highest melt inclusion S concentrations reported for each province, based on the assumption that lower measured sulfur concentrations most likely reflect sulfur degassing. In the case of CAMP, no melt inclusion data are available, and we use sulfur estimated from clinopyroxene-melt sulfur partitioning [Callegaro et al. 2014]. Estimates of sulfur concentrations at sulfide saturation [e.g. Blake et al. 2010;O'Neill 2021] provide an upper limit on magmatic sulfur concentrations for comparison with melt inclusion estimates (Supplementary Material 1, Figure S1).

RESULTS
The CO 2 /S ratios inferred from trace element compositions of individual LIP rock samples (Supplementary Material 2) vary widely, both within individual LIP suites and from one LIP to another (see Supplementary Material 2). For example, in the Siberian Traps (ST), CO 2 /S ratios inferred from Sr/Sm ratios in tholeiitic rocks vary from 0.4 to 43 (Figure 5). Sr/Nd ratios typically yield even wider ranges, shifted to higher CO 2 /S (Supplementary Material 2 and Supplementary Material 3). This variability reflects underlying heterogeneity in trace-element signatures from LIPs, in which very Sr-enriched and Sr-poor samples coexist ( Figure 5; see Ernst [2014]). Crustal contamination, which also varies substantially within each LIP [e.g. Moore et al. 2020], could further contribute to variations in Sr/Sm and Sr/Nd, as discussed below. Modern volcanoes in the calibration dataset exhibit a comparatively smaller variability ( Figure 3).
Each LIP sub-population exhibits close-to-log-normal asymmetric distribution, with positive skewness and overall well defined mode (Figure 4 and Figure 5). Median CO 2 /S ratios for each LIP are listed in Table 1. For the Siberian Traps, median CO 2 /S ratios in tholeiitic rocks are a factor of 5-10 lower than those in alkaline rocks, reflecting likely formation of the alkaline rocks via low degrees of melting of carbonated mantle. Our inferred CO 2 /S for tholeiitic LIP magmas ranges from 0.8 to 2.3 and for alkaline LIP magmas ranges from 5.2 to 24 (Table 1). For comparison, modern tholeiitic continental rift and ocean island magmatic systems (e.g. Hawai ' i or Iceland) have CO 2 /S ratios of 0.3 to 5.6, and modern alkaline systems (continental rift and intraplate volcanoes) have CO 2 /S ratios of 2.1 to 200.
Our inferred LIP parental melt S contents, derived from the peak measured S contents in LIP melt inclusions, span a range from 619-2854 ppm (Table 1; see Supplementary Material 4 for the full melt inclusion compilation from Black et al. [2021]). For comparison, sulfur concentrations estimated from FeO* and the calibration equation of Blake et al. [2010], are more homogenous, and range from 1123 to 1634 ppm (Table 1).
Our estimated parental melt CO 2 contents based on median CO 2 /S in tholeiitic LIP magmas and maximum sulfur in melt inclusions range from 1080-1485 ppm for the Deccan Traps (the most CO 2 -poor LIP) to 4522-7471 ppm for the Siberian Traps (the most CO 2 -rich LIP). For alkaline Siberian Traps magmas, the parental melt CO 2 estimated in this manner is 10,225-23,598 ppm, a factor of~2-5 higher than for tholeiitic rocks of the same LIP, consistent with the hypothesis that elevated CO 2 played an important role in driving eruption of mafic to ultramafic alkaline magmas with limited interaction with the crust [Arndt et al. 1998].

Sources of uncertainty
Our CO 2 /S proxies based on Sr/Sm and Sr/Nd ratios are empirical, and therefore incorporate uncertainties related to the underlying mechanism driving this empirical correlation. The empirical correlation for modern, active volcanoes ( Figure 3) is itself affected by errors and limitations (discussed in Aiuppa et al. [2021]). Among the most important are that (i) the empirical calibration is based on only 12 modern volcanoes for which high-temperature (>450°C) gas composition information is available, and (ii) the gas CO 2 /S and trace element signatures for each calibration volcano are established at the level allowed by (the often sparse and incomplete) information available (as reflected by the relatively large CO 2 /S and Sr/Sm ratio variability at each volcano; Figure 3). Following Aiuppa et al. [2021], we hypothesize that the empirical relationships exhibited by modern volcanism (Figure 3) are imparted by variable extents of metasomatism of the source mantle via the addition of carbonatitic to carbonated silicate melts (see discussion in Aulbach et al. [2020]). These melts are typically calcic (and therefore Sr-rich) and enriched in CO 2 [Dasgupta 2018], so that small additions of these melts to the mantle can lead to the common CO 2 and Sr enrichments exhibited by the mafic melts (that form by mantle melting). The underlying hypothesis is that the source mantle CO 2 /S vs. Sr/Sm and Sr/Nd ratios are inherited by parental mantle melts during melting, and ultimately transferred to volcanic gases released at the surface upon shallow magmatic degassing (as reflected in CO 2 /S ratios), and to erupted rocks (as reflected in Sr/trace element ratios) [Aiuppa et al. 2017;2021].
Analytical uncertainties for whole-rock trace element data are on the order of 1-10 %, and for S concentrations in melt inclusions range from~2 % for NanoSIMS measurements up tõ 10 % for electron microprobe measurements. Analytical uncertainties for S are likely a smaller source of uncertainty than our extrapolation of available melt inclusion measurements of sulfur to estimate sulfur from other units within the same LIP. Melt inclusion data suggest variations in sulfur through the life cycle of LIPs are less pronounced than for other volatiles   Figure 5: Frequency distribution diagrams of CO 2 /S ratios (derived from Sr/Sm and Sr/Nd ratios) and cross-plot of CO 2 /S from Sr/Sm vs Sr/Nd for whole-rock data from the Deccan Traps, the North Atlantic Igneous Province (NAIP), the Siberian Traps, the Parana-Etendeka Traps, the Columbia River Basalts (CRB), and the Central Atlantic Magmatic Province (CAMP). Typical uncertainties in province-wide CO 2 /S from Sr/Sm and Sr/Nd are ±50 % and ±90 % respectively (see Table 1) based on 1-standard deviation variation in Sr/Sm and Sr/Nd ratios from each province.
in the mantle or sulfide saturation in the crust [Wieser et al. 2020]. However, additional data tracking the evolution of sulfur would permit more robust estimates of evolving CO 2 from Sr/Nd and Sr/Sm and implied CO 2 /S ratios. A further source of uncertainty is the extent to which initial CO 2 /S ratios set during melting are modified through mixing and partial CO 2 degassing in deep open-system magma chambers, driving CO 2 -rich flushing of shallower magmas. If this process is more prevalent in the extensive plumbing systems underlying LIPs relative to the modern calibration volcanoes, CO 2 /S ratios in tholeiitic magmas could be higher than implied by trace element ratios and melt inclusion sulfur concentrations. Conversely, if passive degassing is particularly efficient in LIPs, as suggested by comparison with fissure systems like Krafla [Ilyinskaya et al. 2017], CO 2 /S ratios released during eruptive episodes could be lower than expected, with more CO 2 released prior to or between eruptions.
Crustal contamination is also a potential source of uncertainty. Assimilation of Sr-rich, Sm-poor crustal material could modify Sr/Sm and Sr/Nd ratios, obscuring the correlation with gas CO 2 /S. However, our analysis of data from the Columbia River Basalts suggests that this process does not dominate the overall picture from Sr/Sm and Sr/Nd. The degree of crustal contamination is thought to increase from 1-3 % in the Steens to~6 % in the Grande Ronde formation [Wolff et al. 2008;Moore et al. 2020;Day et al. 2021]. Sr/Sm and Sr/Nd in Grande Ronde lavas do not converge towards continental crust-like values (Figure 6), suggesting contamination does not drive the observed evolution.
CO 2 /S ratios derived from alkaline LIP magmas from Sr/Sm versus Sr/Nd generally agree within uncertainty ( Figure 5). For tholeiitic LIP magmas, we find a good match between CO 2 /S implied by both ratios for CO 2 /S ratios between~1 and 10. For more extreme compositions, CO 2 /S from Sr/Sm systematically deviates from CO 2 /S from Sr/Nd, forming an array steeper than the 1:1 line ( Figure 5). The difference in estimated CO 2 /S from the two proxies (Table 1) conveys information on uncertainty in the underlying methodology.
To further assess the fidelity of the LIP CO 2 /S ratios we predict on the basis of Sr/Nd and Sr/Sm ratios, we compare  Hauri et al. 2017;Hirschmann 2018;Miller et al. 2019]. Our estimated CO 2 contents for the tholeiitic Siberian Traps are well above those determined in melt inclusions (white circles with green rims), confirming the degassed nature (pre-and post-entrapment CO 2 loss to gas bubbles) of the latter. For the alkaline Siberian Traps rocks, two separate symbols are used to distinguish estimates that consider (dashed box) or do not consider (solid box) a group of meimechite melt inclusions that have unusually high S concentrations (see Table 1). Modern volcanoes, MORB and DMM compositions are from same sources as in Figure 3 (see Aiuppa et al. [2021] for detailed reference on data sources).
our estimates of CO 2 with estimates based on Ba concentrations (Figure 7). Ba is similarly incompatible to CO 2 during mantle melting, and in conjunction with CO 2 /Ba ratios from melt inclusions suites thought to be undegassed, Ba has been widely applied as a proxy for CO 2 prior to degassing of mantle melts [e.g. Rosenthal et al. 2015;Hauri et al. 2017;Le Voyer et al. 2017;Hirschmann 2018;Hauri et al. 2019;Le Voyer et al. 2019;Miller et al. 2019]. We consider a range in CO 2 /Ba ratios (~48-396) drawn from the range of values in the literature [Rosenthal et al. 2015;Hauri et al. 2017;Miller et al. 2019;Matthews et al. 2020;Hernandez Nava et al. 2021]. To correct for the effects of crystallization on LIP Ba, we derive regressions for Ba vs MgO for each LIP, thereby obtaining an estimate of Ba in parental magmas. We compare the resulting estimates of CO 2 with estimates from Sr/Sm and Sr/Nd ratios ( Figure 6). We find that CO 2 estimates from Sr/Sm and Sr/Nd ratios overlap with estimates from CO 2 /Ba ratios, supporting the validity of our approach.
As summarized in the Introduction, previous constraints on CO 2 concentrations in LIP magmas span a wide range. The new trace element approach presented here provides estimates of median CO 2 from tholeiitic LIP magmas ranging from~1500 ppm for the Deccan Traps up to~4500 ppm CO 2 for the Siberian Traps ( Figure 6). While higher than esti-mates from some melt inclusion suites, particularly datasets that do not account for CO 2 in vapor bubbles (Figure 2), these estimates are somewhat lower than other estimates of LIP CO 2 . For example, recent melt inclusion data from the Deccan Traps and CAMP identify melts with up to~1 wt.% CO 2 [Capriolo et al. 2020;Hernandez Nava et al. 2021]. Self et al. [2006] arrived at an estimate of~0.5 wt.% CO 2 based primarily on historical basaltic eruptions. Data from basaltic fissure eruptions, often seen as an analog for LIP eruptions, range from~4000 ppm CO 2 for Iceland's 2014-2015 Holuhraun eruption [Bali et al. 2018] to~6000 ppm CO 2 for the 1783-1784 Laki eruption [Hartley et al. 2014]. Anderson and Poland [2017] inferred~1 wt.% CO 2 in primary Kīlauea magmas. This 0.4-1 wt.% CO 2 range is not inconsistent with our dataset: if for instance we use the full estimated (from Sr/Sm) CO 2 /S range for the Siberian Traps (0.4 to 43), we would then obtain an estimated parental CO 2 range from as low as 477 ppm to as high as 5.8 wt.%. In other words, while higher (or lower) CO 2 contents can commonly be associated with individual LIP units, the median values still reflect moderate CO 2 for tholeiitic LIP magmas (~4500 ppm, or 0.45 wt.%, for the Siberian Traps) (Figure 7).
If our estimates of parental CO 2 are accurate, they can be combined with fractionation-corrected Ba concentrations to assess CO 2 /Ba ratios compared with those in other settings ( Figure 6). This analysis yields a different picture. In contrast Figure 7: Evolution of CO 2 /S and CO 2 in the earliest three formations of the Columbia River LIP. Steens magmas are tholeiitic to mildly alkaline, while Imnaha and Grande Ronde are tholeiitic in composition. Gray boxes show the 25 th to 75 th percentile range, with median values indicated by a thin black line. While CO 2 /S from Sr/Sm and Sr/Nd differ in the magnitude of CO 2 concentrations, both ratios strongly support evolving parental CO 2 from higher CO 2 in Steens magmas to lower CO 2 in the most voluminous Grande Ronde magmas. These calculations are based on magmatic S concentration of 1900 ppm S, which is the highest S concentration measured in Grande Ronde melt inclusions by Davis et al. [2017]. Steens and Imnaha formations are shown in a lighter gray, to indicate that melt inclusion sulfur data directly from these formations would provide improved constraints on estimates of CO 2 . Sr/Sm and Sr/Nd values for the continental crust are from Rudnick [1995]. Ages of upper Steens and Imnaha and Grande Ronde are from Kasbohm and Schoene [2018].

VOLC
V NIC V 6(1): 129ś145. https://doi.org/10. 30909/vol.06.01.129145 with the moderate median CO 2 concentrations inferred for tholeiitic LIP magmas, CO 2 /Ba ratios for the Siberian Traps and North Atlantic Igneous Province extend to values that rival the highest ratios reported from Iceland [Miller et al. 2019;Matthews et al. 2021]. This combination of moderate CO 2 concentrations in tholeiitic magmas and high CO 2 /Ba could plausibly reflect the joint effects of high CO 2 in the source mantle (at least in some cases), and high degrees of melting during production of main phase tholeiitic magmas [e.g. Herzberg 2004]. How volatile contents vary across mantle reservoirs, including a hypothesized CO 2 -rich deep mantle source for high 3 He/ 4 He [Miller et al. 2019], remains an open question. Additional data characterizing CO 2 in the high-3 He/ 4 He reservoir are needed to assess whether and how such a source might influence the relationship between element ratios and CO 2 .

Diverse, evolving carbon budgets in alkaline and tholeiitic LIP magmas
Ultimately, some LIP magmas-in particular alkaline magmas-are likely CO 2 -rich, whereas others carry substantially less CO 2 . There is probably no single CO 2 concentration that represents all magmas from a given LIP. This is evident within our compilation, where CO 2 /S ratios span 1-2 orders of magnitude among tholeiitic basalts and also among alkaline rocks ( Figure 5, Supplementary Material 2). The large range in modeled CO 2 /S ratios within tholeiitic and alkaline suites from the same LIP underscores the importance of understanding how the budgets of CO 2 and other volatiles evolve through the course of LIP magmatism. Addressing this question is complicated by the challenges of stratigraphic reconstruction across the vast expanses of LIPs. However, for the example of the Columbia River Basalts, where the volcanic stratigraphy is well-established [e.g. Reidel et al. 2013], we explore the evolution of CO 2 /S and CO 2 implied by whole-rock trace element data [Wolff et al. 2008] spanning the first three formations to be emplaced-the Steens, Imnaha, and Grande Ronde. The median CO 2 inferred for Steens parental magmas is 0.7 or 1.4 wt.% CO 2 from Sr/Sm and Sr/Nd respectively, declining to 0.4 or 0.3 wt.% CO 2 respectively for the Grande Ronde ( Figure 6). While the range in CO 2 /S and CO 2 implied by Sr/Sm and Sr/Nd is large, in particular for Steens magmas, median values suggest CO 2 may have evolved substantially through the opening stages of CRB magmatism.
Because variations in LIP CO 2 reflect mantle melting and mixing processes in the LIP plumbing system as well as source characteristics, they may offer deeper insights into how these enormous magmatic systems work. For example, we estimate that alkaline magmas contain up to an order of magnitude higher CO 2 /S ratios relative to tholeiitic magmas. While the erupted volumes of even very CO 2 -rich alkaline magmas are probably too small to trigger major environmental effects [e.g. Ray and Pande 1999;Gales et al. 2020], these rocks may record an important story about tapping of volatile-rich subcontinental mantle lithosphere (SCLM) during LIP magmatism [Guex et al. 2016;Black and Gibson 2019;Gales et al. 2020]. Alkaline LIP magmas are thought to be generated through low-degree (1-3 %) melting of the SCLM [e.g. Gibson et al. 2006].
Although models for the formation of SCLM suggest it originates as the depleted residue of crust extraction [e.g. Jordan 1978], recent work on active rift systems supports the progressive volatile enrichment of long-lived SCLM through metasomatic processes [e.g. Foley and Fischer 2017;Aulbach et al. 2020;Muirhead et al. 2020]. In this case, the volatile systematics and timing of small-volume alkaline LIP melts could be a critical clue to the tempo and nature of volatile release from the SCLM. Although the SCLM has been suggested as a major storage region for both carbon and sulfur [Guex et al. 2016;Foley and Fischer 2017], the relative proportions of volatiles are not known.

The relationship between carbon in LIP magmas and environmental change
LIP carbon outgassing seems to play a central role in events including the end-Permian environmental stress and extinction (EPME) and the End-Triassic mass extinction (ETE)-but metamorphism of sedimentary rocks is often invoked as the primary source of this carbon [e.g. Ganino and Arndt 2009;Svensen et al. 2009;Heimdal et al. 2019]. However, one emerging view for events including the PETM and EPME suggests that a combination of magmatic carbon and 13 C-depleted carbon from sedimentary or surficial sources provides the best explanation for the large mass of carbon injection needed to drive ocean acidification and warming and the modestly 13 Cdepleted isotope signature required to cause negative carbon isotope excursions. In the case of the PETM, Gutjahr et al. [2017] estimated that around 70 % of total CO 2 release derived from the mantle, with the remaining 30 % most likely originating from metamorphism of organic carbon-bearing sedimentary layers in the North Atlantic.
Key factors determining the climate response to LIP-driven mantle carbon release include: 1) the concentration of CO 2 in parental magmas, 2) how that concentration evolves through time, 3) the supply of magma from the mantle, and 4) how that magma supply evolves through time. This work provides new constraints on 1 and 2-the concentration of CO 2 in LIP magmas and how it evolves through time. Melt inclusion data show a decline in melt CO 2 through the course of early Deccan Traps magmatism [Hernandez Nava et al. 2021]. Our analysis hints that a similar evolution may have occurred during the first several formations of the Columbia River Basalts. Unusually high CO 2 in the early Steens magmas compared with later formations (Figure 7) is consistent with the onset of mid-Miocene warming during or preceding emplacement of the Steens formation [Kasbohm and Schoene 2018;Tian and Buck 2022]. Additional melt inclusion sulfur and CO 2 data spanning these formations would help to further test this hypothesis. The rate of surface volcanism has been highlighted as a factor correlated with the severity of mass extinction [Green et al. 2022], but we suggest that surface flux is only part of the puzzle. In particular, our data support parental CO 2 -which both spans a range and evolves through the course of magmatism-as a key variable.

CONCLUSIONS
Unlike CO 2 release from individual Holocene volcanic eruptions, which is negligible relative to the mass of carbon in the ocean and atmosphere [Suarez et al. 2019], the scale of carbon release during emplacement of Large Igneous Provinces is thought to be sufficient to alter the balance of Earth's carbon cycle, in some cases dramatically. Constraining CO 2 carried by LIP magmas is critical to quantifying the overall magnitude of CO 2 release during these episodes and thus the relationship between outgassing, changes in atmospheric pCO 2 , and climate response. Available constraints on CO 2 in LIP magmas derive from melt inclusions, CO 2 /Ba ratios, and comparison with modern basaltic volcanoes [e.g. Self et al. 2006;Black and Gibson 2019;Capriolo et al. 2020]. The latter approaches incorporate significant uncertainties. Melt inclusions are rare in LIP rocks and are prone to entrap melts that have already lost a substantial proportion of their CO 2 . In particular, the rarity of melt inclusions-including the absence of phenocrysts that could host melt inclusions from many main phase LIP flowsmeans that it is challenging to use them as a tool to capture the diversity of CO 2 concentrations within the evolving and diverse suites of magmas that comprise LIPs.
Because our approach relies on the whole-rock geochemistry of LIP rocks, it provides a synoptic perspective that is complementary to the focused view from melt inclusions from one or a few samples. Sr/Sm and Sr/Nd ratios calibrated using a suite of modern volcanoes point to a tremendous diversity in CO 2 /S ratios among LIP magmas. Indeed, while we provide estimates of mean CO 2 for tholeiitic magmas from the Deccan, NAIP, Parana-Etendeka, CAMP, CRB, and Siberian Traps, a major conclusion from our work is that there is not a single CO 2 concentration that fully represents the diverse CO 2 in LIP magmas. As an example of this, we estimate parental CO 2 for the first three formations of the CRB and infer a decline by a factor of 2-5 from the Steens to the Grande Ronde formations, though melt inclusion constraints on sulfur and CO 2 from each of these formations would help to further test this progression. The onset of Miocene warming predates the much more voluminous Grande Ronde Lavas and may coincide with or slightly precede Steens volcanism [Kasbohm and Schoene 2018;Tian and Buck 2022], suggesting that the most CO 2 -rich magmas may drive shifts in climate that are disproportionate with their erupted volume.

AUTHOR CONTRIBUTIONS
Both authors contributed to conceptual development, data analysis, manuscript writing, and creation of figures.