Six-fold increase of atmospheric pCO₂ during the Permian–Triassic mass extinction

Abstract

The Permian–Triassic mass extinction was marked by a massive release of carbon into the ocean-atmosphere system, evidenced by a sharp negative carbon isotope excursion. Large carbon emissions would have increased atmospheric pCO₂ and caused global warming. However, the magnitude of pCO₂ changes during the PTME has not yet been estimated. Here, we present a continuous pCO₂ record across the PTME reconstructed from high-resolution δ¹³C of C₃ plants from southwestern China. We show that pCO₂ increased from 426 +133/−96 ppmv in the latest Permian to 2507 +4764/−1193 ppmv at the PTME within about 75 kyr, and that the reconstructed pCO₂ significantly correlates with sea surface temperatures. Mass balance modelling suggests that volcanic CO₂ is probably not the only trigger of the carbon cycle perturbation, and that large quantities of ¹³C-depleted carbon emission from organic matter and methane were likely required during complex interactions with the Siberian Traps volcanism.

Introduction

The Permian–Triassic mass extinction (PTME; ca. 252 Ma) coincided with rapid global warming that produced one of the hottest intervals of the Phanerozoic^1,2,3,4,5, which was likely triggered by a massive release of greenhouse gases^6,7. The emplacement of the Siberian Traps large igneous province has been widely suggested as the ultimate trigger for the extinction of ~90% of marine species and ~70% of terrestrial vertebrate species at the Permian–Triassic boundary⁸, with major losses amongst plants (e.g. refs. ^9,10). Alongside volcanic degassing, CO₂, SO_2, and halogen volatiles were likely released due to thermal metamorphism by Siberian Traps’ intrusions into organic-rich sediments^6,7,11. The global negative carbon isotope excursion (CIE) found in both marine and terrestrial settings at the PTME (for a review, ref. ¹²) indicates a major carbon cycle perturbation in the ocean-atmosphere system, which implies a rise in the atmospheric CO₂ levels (pCO₂). However, pCO₂ changes during the PTME still remain poorly constrained.

On the one hand, records of pCO₂ from proxies (stomata index, palaeosol carbonates, and biomarkers) are mainly focused on the late Permian and/or Phanerozoic long-term trends without detailed pCO₂ data for the earliest Triassic (refs. ^{13,14,15,16,17}). On the other hand, various models show large variability of peak pCO₂ estimates, because of the different assumed background pCO₂ levels (e.g. refs. ^18,19,20). Hence, there is a pressing need for a continuous proxy-based and high-resolution record of pCO₂ during the PTME. Understanding the magnitude of pCO₂ changes during past hyperthermals is indeed crucial to understand the possible imminent environmental effects of today’s CO₂ increase: pCO₂ has risen from 280 to more than 400 ppmv in the last 150 years and is projected to go higher²¹.

Experiments on living C₃ plants (in the field and in growth chambers) suggest that carbon isotope fractionation (∆¹³C) during photosynthesis increases with increasing CO₂ levels, lowering the carbon isotope signature of C₃ plants (δ¹³C_p)²². Based on this relationship, ∆¹³C calculated from δ¹³C_p measured in fossil C₃ plants remains can be used as a proxy for past pCO₂²³. This proxy successfully reproduced ice-core records of pCO₂ for the Last Glacial Maximum²³, and has been applied to reconstruct pCO₂ during Early Eocene hyperthermals²⁴, the Cretaceous Period²⁵, and the Toarcian Oceanic Anoxic Event²⁶.

Here, we present high-resolution δ¹³C records of fossil C₃ plant remains from sedimentary successions of southwestern China. Using the δ¹³C data of C₃ plants, we calculated a six-fold increase of atmospheric pCO₂ during the PTME, from 426 +133/−96 ppmv to 2507 +4764/−1193 ppmv. Furthermore, the pCO₂ estimates are compared with carbon isotope mass balance calculations showing that in addition to volcanic CO₂, large quantities of ¹³C-depleted carbon emission from organic matter and methane were likely required to trigger the observed global negative CIE in the exogenic carbon pool.

Results and discussion

High-resolution terrestrial carbon isotope records

We present high-resolution terrestrial organic carbon isotope records (δ¹³C_org) from plant cuticles, wood and bulk organic matter (OM) together with our previous work¹⁰ from four terrestrial Permian–Triassic boundary sections (Chahe, Jiucaichong, core ZK4703 and Chinahe) in southwestern China (Supplementary Fig. 1; Supplementary Fig. 2). The δ¹³C of bulk OM and C₃ plant remains from the four study sections exhibit nearly identical secular trends (Fig. 1). Each profile can be divided into four stages: (1) a pre-CIE stage, (2) an onset of the negative CIE (onset of CIE) stage, (3) a prolonged CIE body stage and (4) a post-CIE stage. In the pre-CIE stage, δ¹³C_org records from the Xuanwei Formation are characterized by steady values around −25.0% (Fig. 1). The synchronous, prominent onset of CIEs with peak values of −32% occurs at the bottom of the Kayitou Formation. Subsequently, the onset of the CIE stage is followed by a prolonged interval with sustained low values (ca. −30%) through the whole Kayitou Formation, interrupted by a slight positive shift immediately after the onset of CIE. A recovery to slightly higher δ¹³C_org values (−28% to −26%) starts in the uppermost part of the Kayitou Formation and the Dongchuan Formation. Previously published terrestrial δ¹³C_org profiles in southwestern China (e.g. refs. ^27,28) all belong to mixed organic carbon source in bulk OM. Few unusually negative values (< −34%) observed in the upper Kayitou Formation, e.g., in a published record from Chahe²⁷, are statistical outliers and local signals, as such negative values are not observed in our high-resolution study. These outliers may be caused by local ¹³C-depleted samples possibly containing an algal and/or bacterial component²⁹.

Fig. 1: Carbon isotope excursion trend recorded in global terrestrial C₃ plants and marine carbonates.

The secular carbon isotope excursion (CIE) trend can be divided into four stages (i.e. pre-CIE, onset of CIE, CIE body and post-CIE) in terrestrial bulk organic matter, C₃ plants and marine carbonates, and are shown as different color fields. The last appearance datum (LAD) of coal beds and Gigantopteris flora distributions represent the coal gap and collapse of tropical peatlands respectively^10,45. Carbon isotope (δ¹³C) data source: Chahe (δ¹³C of bulk organic matter from ref. ²⁷; δ¹³C of plants data from this study), Jiucaichong (this study), ZK4703 core and Chinahe (δ¹³C data in this study together with our previous work¹⁰), Amb (Pakistan)³² and global marine carbonate δ¹³C (Methods). The locations of marine and terrestrial carbon isotope profiles are shown in the late Permian palaeogeographic map.

The four-stage terrestrial δ¹³C_org trend is also seen in the marine carbonate carbon isotope (δ¹³C_carb) records (Fig. 1). A total of 10 global-distributed marine Permian–Triassic boundary sections with both high-resolution δ¹³C_carb and conodont biostratigraphy were integrated as a global marine δ¹³C_carb profile, using the age model from the Meishan Global Stratotype Section and Point (GSSP)³⁰ (Supplementary Fig. 3; Supplementary Fig. 4). These newly compiled global δ¹³C_carb records are nearly identical to those published previously (e.g. ref. ¹²).

pCO₂ estimates based on ∆¹³C of fossil plants

Constraining the magnitude of the CIE is crucial to estimate accurate mass, rate, and source of the ¹³C-depleted carbon released during the PTME²⁰. CIE magnitudes show large variations between different localities and substrates because they can be affected by multiple factors³¹. δ¹³C_p profiles from southwestern China (low latitude) and Pakistan³² (middle latitude) exhibit CIE magnitudes of ca. −7% and ca. −5.5% respectively, which are significantly larger than the ca. −3.5% marine CIE magnitude estimated from global marine δ¹³C_carb records (Fig. 1). Data compilation confirms this discrepancy: terrestrial CIE magnitudes range from −3.6% to −6.1% (bulk OM, 25th percentile to 75th percentile, n = 29), and from −5.2% to −7.1% (C₃ plants, n = 9), whereas marine CIE magnitudes range from −3.0% to −4.7% (n = 69) (Fig. 2; Supplementary Table 1). As shown both in modern and fossil plants, elevated atmospheric pCO₂ was likely responsible for amplifying the magnitude of the CIE in the terrestrial δ¹³C_p record due to an increase of ∆¹³C^22,33. Therefore, following the relationship between ∆¹³C and pCO₂ developed by Cui and Schubert²⁴ (Methods), we could calculate the pCO₂ across the PTME. The ∆¹³C was calculated using the δ¹³C_p records of four study sections from southwestern China, and the δ¹³C_CO2 (the δ¹³C of atmospheric CO₂; Supplementary Fig. 5) calculated from the global marine δ¹³C_carb compiled in this study. As explained above, this is possible because the marine and terrestrial δ¹³C records are closely comparable and can be readily correlated (Fig. 1), the correlation being supported also by biostratigraphy (flora and conchostracans), and radioisotope dating (Supplementary Fig. 6; Supplementary Information). The initial, background late Permian pCO_2(t = ₀₎ is set in our calculations at 425 ± 68 ppmv based on the late Changhsingian pCO₂ estimates calculated by Li et al.¹⁶ using stomatal ratio method and mechanistic gas exchange model for fossil conifers from the Dalong Formation in South China, with good age control and reliable taxonomy.

Fig. 2: Boxplot of carbon isotope excursion magnitudes for three substrates.

Carbon isotope excursion (CIE) magnitudes of marine carbonate, terrestrial bulk organic matter (OM), and terrestrial C₃ plant compiled from the literature and this study. The magnitude of the terrestrial CIE is larger compared to the marine CIE magnitude. The Wilcoxon test suggests that the CIE magnitude between marine and terrestrial substrate is statistically different (Supplementary Table 1, p < 0.001). A Kruskal-Wallis test further shows the significant difference of CIE among marine carbonate, terrestrial bulk organic matter and C₃ plant groups (p < 0.001). The “n” value represents the number of δ¹³C profiles.

Our estimates (Fig. 3) show that pCO₂ was moderately low (426 +133/−96 ppmv) at 252.1 Ma within the pre-CIE stage (upper part of conodont Clarkina changxingensis zone). Subsequently, the pCO₂ began to increase rapidly in the Clarkina yini zone, reaching a maximum level (2507 +4764/−1193 ppmv), immediately after the Permian–Triassic boundary (Hindeodus parvus zone). This near six-fold increase of atmospheric pCO₂ occurred within ~75 kyr and coincided with the onset of the global CIE. The pCO₂ remained high (ca. 1500 to 2500 ppmv) immediately after the onset of the CIE, with only one transient drop (down to ca. 1300 ppmv). Coupled to the recovery of δ¹³C, pCO₂ drops to ca. 700 ppmv at the top of Isarcicella isarcica zone. Atmospheric CO₂ levels show a close coupling with estimated sea surface temperatures (r = + 0.60, p < 0.001, n = 173; Supplementary Fig. 7), implying that CO₂ was likely the dominant greenhouse gas across the PTME, although the contribution of other greenhouse gases such as methane and water vapor cannot be excluded here. The six-fold increase of atmospheric pCO₂, together with a 10 °C increase in sea surface temperatures estimated from low latitude conodont oxygen isotope (Fig. 3) implies Earth system sensitivity (ESS) of 3.9 °C per doubling of CO₂ if we assume ESS equals to ∆T/log₂[pCO_2(peak)/pCO_{2(background)}]³⁴. This is consistent with a previous estimate of the Permian–Triassic ESS³⁵ and the IPCC equilibrium climate sensitivity range of 1.5 to 4.5 with a median of 3.0³⁶, suggesting slow feedbacks operated in the geologic past. However, climate model simulations reveal that the increase of SST in high latitude should be higher than low latitude³⁷. As a result, the 10 °C SST increase in low latitude might underestimate the global SST increase, which leads to an underestimate of the Earth system sensitivity during the PTME.

Fig. 3: Summary of Permian–Triassic boundary proxy data and reconstructed pCO₂ changes.

The radiometric ages are from the Meishan section³⁰. Conodont zones are those of the Meishan section. Global marine carbonate carbon isotope (δ¹³C_carb) compiled from ten sections (Methods). Land C₃ plant carbon isotopes profile (δ¹³C_p) is from the four study sections in southwestern China (Fig. 1). Sea surface temperature (SST) was calculated based on conodont δ¹⁸O values from South China (Meishan and Shangsi)^1,2,3, Iran (Kuh-e-Ali Bashi and Zal)⁴ and Armenia (Chanakchi)⁵. The blue, green and red lines represent the LOESS fit curve for δ¹³C_carb, δ¹³C_p and SST, respectively, while light blue, green, and red shaded area represent 68% confidence intervals (standard errors calculated from LOESS). Reconstruction of atmospheric pCO₂ based on carbon isotope fractionation in C₃ land plant (on a log scale). Median values of the 10,000 re-samplings determined by Monte Carlo uncertainty propagation are shown as dark gray line. The 68% confidence intervals for pCO₂ are showed as light gray shaded area (lower limit and upper limit represent the 16^th and 84^th percentiles respectively). Previous reported pCO₂ estimates based on stomata^16,17, palaeosol carbonates^13,14 and phytane¹⁵ are shown as points with error bar (Supplementary Table 2). Marine species richness data show the two pulse mass extinction⁸. I.―Isarcicella; C. c―Clarkina changxingensis; C. y―Clarkina yini; C. m―Clarkina meishanensis; H. c―Hindeodus changxingensis; C. t―Clarkina taylorae; H. p―Hindeodus parvus.

Comparison with previous studies and uncertainty

Previous pCO₂ estimates around the Permian–Triassic boundary (Fig. 3; Supplementary Table 2) come from stomatal proxies^16,17, palaeosol carbonates^13,14, phytane¹⁵ and carbon cycle modelling (e.g. refs. ^18,19,20). Published proxy-based pCO₂ reconstructions are mostly for the late Permian, within long-term and very low-resolution Phanerozoic records. Stomata-based estimates from modified fossil Ginkgo stomatal index method¹⁷ gave pCO₂ around 400–800 ppmv in the latest Permian, but with poor age constraint and high taxonomic uncertainty¹⁶. Latest Permian pCO₂ from δ¹³C of palaeosol carbonates from Texas, US¹³, was calculated at 400 ppmv^38,39 (re-calculated by ref. ³⁸ correcting the assumed soil respired CO₂ concentration), but latest Permian palaeosol carbonate record from the Karoo Basin¹⁴ shows higher values (883–1325 ppmv). Similarly, the δ¹³C_phytane-based pCO₂ estimates show that CO₂ levels during Changhsingian could have ranged from 873 to 1085 ppmv¹⁵. The few earliest Triassic peak pCO₂ estimates from stomatal¹⁷ and phytane¹⁵ proxies show significant variation (600–2100 ppmv). Simulations with various climate models (e.g. carbon cycle box modelling^18,19 and cGENIE²⁰) show major variability of peak pCO₂ values (1000–9380 ppmv; Supplementary Table 3), using a large range of assumed background pCO₂.

Several effects, especially diagenesis⁴⁰, chemical treatment⁴¹, plant taxonomic changes⁴² and precipitation^43,44 can influence the δ¹³C_p and consequently affect pCO₂ estimates. The original signals of δ¹³C_p values can potentially be altered by diagenesis during burial⁴⁰ and chemical treatment during sample preparation⁴¹. However, the method we use to calculate palaeo-pCO₂ considers a relative change of the ∆¹³C that minimizes these biases (Methods). A dramatic plants turnover occurred in southwestern China during the PTME, with a Gigantopteris flora (spore plant) in the Xuanwei and basal Kayitou formations replaced by an Tomiostrobus (spore plant) and Peltaspermum (seed plant) dominated flora⁴⁵. Experiments on modern plants indicate lower ∆¹³C in seed plants than in spore plants⁴². Using a plant assemblage including a mixture of different taxa and plant tissues is better than using single species and plant remains when using δ¹³C_p as pCO₂ proxy³³. In this study we used a mixture of different plant tissues (i.e. cuticle, charred wood and non-charred wood), which very likely includes different plant taxa.

An increase of the mean annual precipitation (MAP) can also increase ∆¹³C^44,46. This effect is negligible in sites experiencing high precipitation (>1500 mm/yr)⁴⁷, such as the studied area in southwestern China, which was a humid, equatorial peatland during the PTME⁴⁵. The plant community changed from Gigantopteris flora-dominated rainforest ecosystem to isoetalean-dominated (lycophyte) herbaceous vegetation that inhabited the surrounding margins of coastal oligotrophic lakes, which indicate fairly constant precipitation regimes during the PTME interval^48,49. The sedimentology of the Xuanwei and Kayitou formations suggests there was no significant precipitation change across the mass extinction (Supplementary Fig. 8; ref. ⁵⁰). In contrast, low MAP can explain the smaller magnitude of the CIE (<3%) recorded at the PTME in the semi-arid locations of Karoo Basin and North China³¹. In summary, the persistently humid condition in southwestern China was unlikely to have affected plant ∆¹³C, thus the pCO₂ estimates are considered robust. A Monte Carlo method has been applied to evaluate the uncertainties (Supplementary Information; Supplementary Fig. 9), which reveals that the uncertainty in the pCO₂ increases with increasing pCO₂, as seen in the previous studies⁵¹.

Potential source of ¹³C-depleted carbon during the PTME

The ultimate source of ¹³C-depleted carbon capable to trigger the observed negative CIE, is widely debated. Several climate models of varying complexities (e.g. simple box models^18,19 and cGENIE²⁰) use different light carbon sources to fit the δ¹³C of marine carbonates (Supplementary Table 3). Proposed ¹³C-depleted carbon sources include biotic or thermogenic methane (δ¹³C ≈ −60% to −40%; e.g. ref. ¹⁸), CO₂ from thermal metamorphism or rapid oxidation of organic-rich rock (δ¹³C ≈ −25%; e.g. ref. ^6,19,52,53), and volcanic CO₂ (δ¹³C ≈ −6%; e.g. ref. ⁵⁴) or a combination of these sources²⁰. We performed a simple carbon isotope mass balance to evaluate the most likely ¹³C-depleted carbon source^55,56. Under the assumption of four possible ¹³C-depleted carbon sources (i.e. volcanic CO₂, organic matter, thermogenic methane, and biogenic methane), the mass of released carbon was calculated (Fig. 4) and compared with our pCO₂ rise estimates (2081 +4764/−1193 ppmv). Our calculated pCO₂ mostly falls within the range of model results for organic matter and methane release scenarios (Fig. 4), supporting the hypothesis that these more ¹³C-depleted sources than volcanic CO₂ are required to contribute to the global carbon cycle perturbation. There are some U-Pb dating⁷ and field evidence^6,57 show that the organic-rich sediment intruded by Siberian Traps sill likely provided massive ¹³C-depleted CO₂ and thermogenic methane, which may have been the ultimate trigger of the global CIE and significant increase in atmospheric CO₂. However, due to the limitation of the C₃ plant proxy, the uncertainty of pCO₂ is significantly larger at high CO₂ levels (Supplementary Fig. 9). Therefore, volcanic CO₂ source could still have made a contribution to the global carbon cycle perturbation.

Fig. 4: Mass of added carbon estimated from carbon isotope mass balance calculation.

Four different scenarios including volcanic CO₂ (δ¹³C = −6%), organic matter (δ¹³C = −25%), thermogenic methane (δ¹³C = −40%) and biogenic methane hydrate (δ¹³C = −60%). Second y-axis converts the mass of added carbon to an increase in atmospheric pCO₂ based on the earth system model (1 Gt C = 0.3 ppmv CO₂)^55,56. Gray shaded area represents the 68% confidence intervals of pCO₂ increase (2081 +4764/−1193 ppmv) estimated from the C₃ plant proxy.

The best estimates for mass of added carbon based on a 3.5% carbonate CIE magnitude and a source with δ¹³C of −25% to −60%, suggest that at least 3900~12,000 Gt carbon were added into the ocean-atmosphere system during the PTME. Previous estimates (15,000–20,000 Gt C) were based on an assumed ca. 5.5% negative shift of C₃ plant in simple mass balance calculations³² and might therefore have overstated the amount of added carbon. The ca. 7% CIE in C₃ plants, amplified by pCO₂ increase, also produces an over-estimate in the mass balance calculation (Fig. 4). Our estimates of the amount of injected carbon are also smaller than those calculated by the cGENIE climate model (7,000~22,400 Gt C)²⁰, because the ~5% magnitude of δ¹³C_carb from Meishan used in the calculations is too large compared to the global carbonate records. However, simple mass balance calculations don’t consider global carbon cycle fundamental processes and changes through time, like carbon weathering and burial rates during the studied interval. In addition, the size of the DIC reservoir is usually assumed to be the size of the background surface carbon reservoir, because of poor understanding of atmosphere carbon reservoir size⁵⁸. These limitations might lead to an underestimate of the total mass of added CO₂.

Carbon emission caused prolonged high pCO₂ and high temperature (ca. 35 °C) during the earliest Triassic (H. parvus and I. isarcica zones) and may have lasted for > 500 kyr (Fig. 3). This lengthy phase of extreme warmth likely implies prolonged carbon emissions into ocean-atmosphere system from continued eruption of the Siberian Traps volcanism, and/or reduced carbon sequestration rate, potentially due to lower consumption of atmospheric CO₂ through reduced organic carbon burial and the possible failure of the silicate weathering thermostat⁵⁹.

Methods

Sample treatment and analysis

In total, 68 samples from Chinahe, 41 samples from ZK4703 and 40 samples from Jiucaichong were analyzed for bulk organic carbon isotopes. Samples were crushed to fine powder (<200 mesh), and ∼2 g powder were weighed, placed into a centrifuge tube and treated with 3 mol/L HCl for 24 h to remove the carbonate. Then the treated samples were rinsed with ultrapure water repeatedly until neutralized and finally dried at 35 °C. For C₃ plants δ¹³C analysis, 45 samples from Chinahe, 26 samples from ZK4703, 30 samples from Jiucaichong and 13 samples from Chahe were treated with concentrated HCl and HF, then sieved over 500 μm and a 100 μm mesh screen to get the 100~500 μm particles. C₃ plant fragments, including cuticle, non-charred wood and charred wood (charcoal), were picked under the microscope. The δ¹³C_org analyses were performed by using an elemental analyzer (EA) coupled to an isotope ratio mass spectrometer (Thermo Delta V Advantage) at the State Key Laboratory of Biogeology and Environmental Geology of the China University of Geosciences (Wuhan). The results were calibrated using certified secondary references standards: USGS40 (δ¹³C = −26.39%) and UREA (δ¹³C = −37.32%) and given in per mil (%) relative to Vienna Pee Dee Belemnite (VPDB) with analytical precision better than ± 0.2%. A Multi EA 4000-analyzer was used for TOC at China University of Geosciences (Wuhan), yielding an analytical precision of 1.5%.

Carbon isotope compilation and estimate of CIE magnitude

In order to estimate a reliable magnitude of the CIE, the carbon isotope profiles that record a roughly complete CIE shape with pre-CIE and CIE body are selected in our study. The compilation consists of 69 marine carbonate carbon isotope (δ¹³C_carb) profiles and 38 terrestrial δ¹³C_org profiles. The δ¹³C_carb profiles recording complete negative CIE are from Eastern Palaeotethys (n = 29), Western Palaeotethys (n = 19), Central Palaeotethys (n = 4), Northern Neotethys (n = 4), Southern Neotethys (n = 10) and Panthalassa (n = 3). Bulk marine organic matter δ¹³C records were not included, because they often represent a mix of various organic components (both marine and terrestrial). The sedimentary facies belong to a range of shallow shelf, deep shelf, and slope environments. The few reported δ¹³C_carb profiles from deep basins are ignored in this compilation (e.g. Shangsi section), because the elevated water stratification and large vertical δ¹³C DIC gradients at deep basin sites during Permian–Triassic crisis could cause large CIE magnitudes⁶⁰. A total of 38 terrestrial δ¹³C_org records are reviewed from eight terrestrial basins including western Guizhou and eastern Yunnan in southwestern China (n = 14), Junggar Basin (n = 3), Turpan Basin (n = 1), North China (n = 3), Central European Basin (n = 1), Bowen Basin (n = 2), Sydney Basin (n = 7), Karoo Basin (n = 1) and three oceanic regions where organic matter (OM) in samples are C₃ plants or a mix of organic matter dominated by C₃ plants including South China (n = 1), Boreal realm (n = 2) and South Neotethys (n = 3). Among these terrestrial δ¹³C_org profiles, there are nine records of δ¹³C records from C₃ plant (5 δ¹³C_wood and 4 δ¹³C_cuticle) from Meishan section, Amb section in South Neotethys, southwestern China, and others are all bulk δ¹³C_org profiles.

In order to demonstrate the difference of marine and terrestrial CIE magnitudes, carbon isotope values immediately before the CIE (δ¹³C_background) and peak values (δ¹³C_peak) are used to calculate the magnitude of the CIE (δ¹³C_peak − δ¹³C_background). Note that 31 pairs of δ¹³C_background and δ¹³C_peak values are from marine sections that are well constrained by latest Permian conodont occurrences (e.g. C. changxingensis, H. praeparvus, H. latidentatus zones) and earliest Triassic conodont (H. parvus and I. isarcica zones) occurrences. To test if the discrepancy of the CIE magnitude in different substrates (marine carbonate, terrestrial bulk OM, terrestrial C₃ plant tissues) is statistically significant, we used a non-parameter Kruskal-Wallis test (function kruskal.test), using R software. The Wilcoxon (function wilcox.test) test was performed in R software to determine whether means of two independent groups (marine vs. terrestrial) are equal or not. Boxplots were drawn to visualize discrepancy in CIE magnitude of different substrates. All statistical analyses and graphing functions were undertaken using R.

C₃ plant proxy

The carbon isotope fractionation in C₃ plants (∆¹³C) and atmospheric pCO₂ is described as a hyperbolic relationship^22,23,24,61:

$${\Delta} ^{13}{\mathrm{C}} = \frac{{\left( {\mathrm{A}} \right)\left( {\mathrm{B}} \right)\left( {p{\mathrm{CO}}_{\mathrm{2}} + {\mathrm{C}}} \right)}}{{{{{\mathrm{A}} + }}\left( {\mathrm{B}} \right)\left( {p{\mathrm{CO}}_2 + {\mathrm{C}}} \right)}}$$

(1)

The original δ¹³C signals in C₃ plant can be altered by several effects (e.g. diagenesis⁴⁰, chemical treatments⁴¹), that potentially influence pCO₂ calculations. In order to minimize this effect, the data set is analyzed by a relative change in the ∆¹³C value between the time of interest (t) and a reference time (t = 0), designated as ∆ (∆¹³C):

$${\Delta} \left( {{\Delta} ^{13}{\mathrm{C}}} \right) = {\Delta} ^{13}{\mathrm{C}}_{\left( t \right)} - {\Delta} ^{13}{\mathrm{C}}_{\left( {t = 0} \right)}$$

(2)

which can be expanded as:

$${\Delta} ({\Delta} ^{13}{\mathrm{C}}) = \frac{{\left( {\mathrm{A}} \right)\left( {\mathrm{B}} \right)\left( {p{\mathrm{CO}}_{2\left( t \right)} + {\mathrm{C}}} \right)}}{{{\mathrm{A}} + \left( {\mathrm{B}} \right)\left( {p{\mathrm{CO}}_{2\left( t \right)} + {\mathrm{C}}} \right)}} - \frac{{\left( {\mathrm{A}} \right)\left( {\mathrm{B}} \right)\left( {p{\mathrm{CO}}_{2\left( {t = 0} \right)} + {\mathrm{C}}} \right)}}{{{\mathrm{A}} + ({\mathrm{B}})\left(p{\mathrm{CO}}_{2\left( {t = 0} \right)} + {\mathrm{C}}\right)}}$$

(3)

By rearranging Eq. (3), pCO_2(t) at any given time can be calculated by

$$p{\mathrm{CO}}_{2(t)} = \frac{{{\Delta} \left( {{\Delta} ^{{\mathrm{13}}}{\mathrm{C}}} \right)\cdot {\mathrm{A}}^2 + {\Delta} \left( {{\Delta} ^{{\mathrm{13}}}{\mathrm{C}}} \right) \cdot {\mathrm{A}} \cdot {\mathrm{B}} \cdot p{\mathrm{CO}}_{2\left( {t = {\mathrm{0}}} \right)} + {\mathrm{2}} \cdot {\Delta} \left( {{\Delta} ^{{\mathrm{13}}}{\mathrm{C}}} \right) \cdot {\mathrm{A}} \cdot {\mathrm{B}} \cdot {{{\mathrm{C}} + }}{\Delta} \left( {{\Delta} ^{{\mathrm{13}}}{\mathrm{C}}} \right) \cdot {\mathrm{B}}^2 \cdot {\mathrm{C}} \cdot p{\mathrm{CO}}_{2\left( {t = {\mathrm{0}}} \right)} + {\Delta} \left( {{\Delta} ^{{\mathrm{13}}}{\mathrm{C}}} \right) \cdot {\mathrm{B}}^2 \cdot {\mathrm{C}}^2 + {\mathrm{A}}^2 \cdot {\mathrm{B}} \cdot p{\mathrm{CO}}_{2\left( {t = {\mathrm{0}}} \right)}}}{{{\mathrm{A}}^2 \cdot {\mathrm{B}} - {\Delta} \left( {{\Delta} ^{{\mathrm{13}}}{\mathrm{C}}} \right) \cdot {\mathrm{A}} \cdot {\mathrm{B}} - {\Delta} \left( {{\Delta} ^{{\mathrm{13}}}{\mathrm{C}}} \right)\cdot {\mathrm{B}}^2 \cdot p{\mathrm{CO}}_{2\left( {t = {\mathrm{0}}} \right)} - {\Delta} \left( {{\Delta} ^{{\mathrm{13}}}{\mathrm{C}}} \right) \cdot {\mathrm{B}}^2 \cdot {\mathrm{C}}}}$$

(4)

where A, B, C are curve fitting parameters. Values for A and B are 28.26 ± 0 and 0.22 ± 0.028, respectively⁵¹, which could produce more robust pCO₂ estimates compared with other parameter values in subsequent research³³. The C is the function of the A and B values [C =A×4.4/((A − 4.4) × B)]. The pCO_2(t = 0) is equal to the pCO₂ level before the negative CIE, determined from independent stomatal proxies based on fossil conifers from the Dalong Formation in South China¹⁶. Because of the good age control (Clarkina changxingensis conodont zone), reliable taxonomy and calculation method, these stomatal estimates are considered as robust pCO₂ estimates before CIE. The mean value for the stomatal estimates is 425 ± 68 ppmv set as pCO_2(t = 0). The ∆¹³C is the carbon isotope fractionation between atmospheric CO₂ and plant organic carbon (${\Delta}^{{\mathrm{13}}}{\mathrm{C}} = ( {{\delta}^{{\mathrm{13}}}{\mathrm{C}}_{{\mathrm{CO}}_2} - {\delta}^{{\mathrm{13}}}{\mathrm{C}}_{{\mathrm{p}}}} ){\mathrm{/}}( {{\mathrm{1}} +{\delta}^{{\mathrm{13}}}{\mathrm{C}}_{{\mathrm{p}}}/{\mathrm{1000}}} )$). Thus, the ∆(∆¹³C) can be calculated by

$${\Delta} \left( {{\Delta} ^{{\mathrm{13}}}{\mathrm{C}}} \right) = \; \left( {{\delta}^{{\mathrm{13}}}{\mathrm{C}}_{{\mathrm{CO}}_2(t)} - {\delta}^{{\mathrm{13}}}{\mathrm{C}}_{{\mathrm{p}}(t)}} \right){\mathrm{/}}\left( {{\mathrm{1}} + {\delta}^{{\mathrm{13}}}{\mathrm{C}}_{{\mathrm{p}}(t)}/{\mathrm{1000}}} \right) \\ \quad- \left( {{\delta}^{{\mathrm{13}}}{\mathrm{C}}_{{\mathrm{CO}}_2(t = {\mathrm{0}})} - {\delta}^{{\mathrm{13}}}{\mathrm{C}}_{{\mathrm{p}}(t = {\mathrm{0}})}} \right){\mathrm{/}}\left( {{\mathrm{1}} + {\delta}^{{\mathrm{13}}}{\mathrm{C}}_{{\mathrm{p}}(t = {\mathrm{0}})}/{\mathrm{1000}}} \right)$$

(5)

where ${\delta}^{{\mathrm{13}}}{\mathrm{C}}_{{\mathrm{p}}(t = {\mathrm{0}})}$ and δ¹³C_p(t) are δ¹³C values in C₃ plant at reference time (t = 0) and the time of interest (t). The values for ${\delta}^{{\mathrm{13}}}{\mathrm{C}}_{{\mathrm{p}}(t = {\mathrm{0}})}$ is determined as −24.42 ± 0.5%, whose age equals to Clarkina changxingensis conodont zone that occurred slightly earlier than the onset of the CIE¹⁶. We suggest that a mixture of δ¹³C in C₃ plant cuticle, charred wood and non-charred wood from southwestern China (without δ¹³C of bulk OM) provides the best choice as δ¹³C_p(t) input data for three reasons. Firstly, using the δ¹³C values of C₃ plant tissues (e.g. cuticle, wood) can minimize the influence of varying OM sources from mixed soils and sediments. Several previous reports on terrestrial δ¹³C_org in western Guizhou and eastern Yunnan, South China have recorded the negative CIE^27,28,62,63, but all the data are not δ¹³C from C₃ plants and not suitable for pCO₂ calculation. Secondly, Eq. (1) is based on the combination of carbon isotope from stem and leaf tissues of chamber plants. Thirdly, the mixture of different micro plant tissues (i.e. cuticle, charred wood and non-charred wood) would contain different plant fossils species that is suggested to be better than a single species approach when applying this proxy³³.

The ${\delta}^{{\mathrm{13}}}{\mathrm{C}}_{{\mathrm{CO}}_2(t = 0)}$ and ${\delta}^{{\mathrm{13}}}{\mathrm{C}}_{{\mathrm{CO}}_2(t)}$ are δ¹³C values in atmospheric CO₂ at reference time (t = 0) and the time of interest (t). The temperature (T) dependent carbon isotope fractionation between dissolved inorganic carbon (DIC) and atmospheric CO₂⁶⁴ can be used to calculate ${\delta}^{{\mathrm{13}}}{\mathrm{C}}_{{\mathrm{CO}}_2}$.

$${\delta}^{{\mathrm{13}}}{\mathrm{C}}_{{\mathrm{CO}}_2} =\, {\delta}^{{\mathrm{13}}}{\mathrm{C}}_{{\mathrm{DIC}}} - \left( {{\mathrm{0}}{\mathrm{.91}} \times \left( { - {\mathrm{0}}{\mathrm{.1141}} \times {\mathrm{T}} + {\mathrm{10}}{{.78 }}} \right) + {\mathrm{0}}{\mathrm{.08}} \times \left( { - {\mathrm{0}}{\mathrm{.052}} \times {\mathrm{T}} + {\mathrm{7}}{{.22}}} \right)} \right)$$

(6)

where T is the sea surface temperature determined from oxygen isotopes of conodont fossils^1,2,3,4,5. δ¹³C_DIC can be estimated from marine δ¹³C_carb (δ¹³C_DIC = δ¹³C_carb − 1%), because the carbon isotope fractionation between marine carbonate (δ¹³C_carb) and dissolved inorganic carbon (δ¹³C_DIC) is constant and independent of temperature (~1%)⁶⁵. Among the global CIE compilations, 10 marine, high-resolution, non-basinal δ¹³C_carb profiles are well constrained by detail conodont zones including Meishan³⁰, Nhi Tao⁶⁶, Yangou⁶⁷ in eastern Palaeotethys; Zal³, Kuh-e-Ali Bashi³ in central Palaeotethys; Bálvány North⁶⁸ in western Paloetethys; Shahreza¹², Abadeh¹² in northern Neotethys; Wadi Shahha⁶⁹, Wenbudangsang⁷⁰ in Southern Neotethys. Thus, we integrated these 10 δ¹³C_carb profiles together as a global marine δ¹³C_carb profile combined with a U-Pb age model³⁰ and high-resolution conodont zones (conodont zones from Meishan are selected as standard^71,72). LOESS curves with 0.002 Myr spacing were fitted to the integration of global marine δ¹³C_carb. At each 0.002 Myr time step, the probability maximum value and standard error are identified and served as δ¹³C_carb input parameters in calculations. The best degree of smoothing for LOESS fitting was determined using cross-validation method in package fANCOVA. To eliminate the potential for an uneven distribution of δ¹³C_carb data, we also applied a LOESS fitting based on an 80% subsample of all data. In addition, the δ¹³C_carb data from Meishan (n = 199) is the most abundant of all the δ¹³C_carb data (n = 707), thus, we performed a LOESS fitting based on δ¹³C_carb data without Meishan data (Supplementary Fig. 4).

In order to calculate pCO_2(t), we need to align global marine δ¹³C_carb profiles and δ¹³C_p based on same age model. The nearly same CIE curves were divided into four stages in carbonate and C₃ plants records to ensure the correlation between marine and terrestrial carbon isotope profiles. The age model for four sections is showed in Supplementary Information. In addition, the LOESS method with 0.002 Myr spacing was also performed in δ¹³C_p and temperature data to get the probability maximum value and standard error at each 0.002 Myr time step. The Monte Carlo method was employed to propagate input error⁵¹ by the propagate package in R. All the input parameters were assumed to be Gaussian distributed with mean and standard deviations listed in Supplementary Table 4. 10,000 values for each input parameters were randomly sampled to calculate 10,000 values for each pCO_2(t). The invalid pCO_2(t) values (i.e., pCO_2(t) < 0 or >10⁶ ppmv) were excluded. The 16^th and 84^th percentiles of the remaining estimates were determined to construct the 68% confidence interval. The positive error of the reconstructed pCO_2(t) value represents the difference between the 84th percentile value and the median, and the negative error represents the difference between the 16th percentile value and the median. The sensitivity analysis of C₃ plant proxy is discussed in Supplementary information and Supplementary Fig. 9.

Carbon isotope mass balance

This model used to evaluate the light carbon source, following mass balance equation is modified from McInerney and Wing⁵⁵:

$${\mathrm{M}}_{{\mathrm{added}}} = \frac{{\left( { - {\mathrm{CIE}} \times {\mathrm{M}}_{{\mathrm{background}}}} \right)}}{{\left( {{\delta}^{{\mathrm{13}}}{\mathrm{C}}_{{\mathrm{peak}}} - {\delta}^{{\mathrm{13}}}{\mathrm{C}}_{{\mathrm{added}}}} \right)}}$$

(7)

where M_added is the mass of carbon added into atmosphere-ocean system carbon emission. The M_background represents initial carbon reservoir size during Permian–Triassic including ocean and atmosphere carbon inventory, but dominated by the ocean reservoir. Thus, the M_background is assumed to be the initial marine DIC reservoir size ranging from 66,000 to 82,000 Gt^58,73. CIE represents the global magnitude of CIE controlled only by release of light carbon effect, which is set as a series values from −1% to −8%. The peak δ¹³C value (δ¹³C_peak) at the event is calculated by initial isotopic composition of global carbon reservoir (δ¹³C_background) and CIE (δ¹³C_peak = δ¹³C_background + CIE). The δ¹³C_background is assumed to be the initial isotopic composition of DIC reservoir 2.2% that is estimated from global marine δ¹³C_carb profiles (age >252.104 Ma). The δ¹³C_added is the δ¹³C value of the carbon source causing the CIE. Four kinds of carbon sources are involved including biogenic methane buried in permafrost or seafloor (δ¹³C = −60%), thermogenic methane (δ¹³C = −40%), thermal metamorphism or rapid oxidation of organic-rich rock (δ¹³C = −25%) and CO₂ released from direct volcanic eruption (−6%). Finally, the increased pCO₂ is estimated from M_added (1 Gt C = 0.3 ppmv; ref. ⁵⁶), and compared with reconstructed atmospheric CO₂ levels from C₃ plant proxy.