Quantifying ancient atmospheric pCO2 provides valuable insights into the interplay between greenhouse gases and global climate. Beyond the 800-ky history uncovered by ice cores, discrepancies in both the trend and magnitude of pCO2 changes remain among different proxy-derived results. The traditional paleosol pCO2 paleobarometer suffers from largely unconstrained soil-respired CO2 concentration (S(z)). Using finely disseminated carbonates precipitated in paleosols from the Chinese Loess Plateau, here we identified that their S(z) can be quantitatively constrained by soil magnetic susceptibility. Based on this approach, we reconstructed pCO2 during 2.6–0.9 Ma, which documents overall low pCO2 levels (<300 ppm) comparable with ice core records, indicating that the Earth system has operated under late Pleistocene pCO2 levels for an extended period. The pCO2 levels do not show statistically significant differences across the mid-Pleistocene Transition (ca. 1.2–0.8 Ma), suggesting that CO2 is probably not the driver of this important climate change event.
Over the last 3 million years (Ma), the Earth has cooled substantially and transitioned from a single-pole glaciation to a stage with major glaciations on both poles. In the past 1 Ma, the period of glacial cycles switched from ~41 thousand years (ky) to ~100 ky (mid-Pleistocene Transition, MPT), with the magnitude of the climate change associated with the glacial cycles significantly enhanced1,2. What has ultimately driven these far-reaching climate changes is unclear. Atmospheric CO2, the most important non-condensing greenhouse gas, plays an important role in global climate changes. However, although an overall decreasing trend has been documented, the available early Pleistocene (2.6–0.8 Ma) pCO2 reconstructions, mostly from the marine realm, differ for both trends and absolute values3.
As a terrestrial archive, the pedogenic carbonates found in paleosols have been widely applied for pCO2 reconstruction4, especially for the Paleozoic and Mesozoic eras when other proxies are often not available5. In soils, the rate of carbonate crystallization is much slower than gas exchange, thus pedogenic carbonates precipitated in the vadose zone are thought to reach carbon isotopic equilibrium with CO2 in soil pore space6. This soil-pore CO2 represents a mixture of two end members with distinct δ13C signatures: atmospheric CO2 and soil-respired CO2. Built on this isotopic end-member mixing principal and gas diffusion dynamics, previous studies have derived a complete solution to estimate ancient atmospheric pCO2 from soil-associated parameters (i.e. the paleosol CO2 paleobarometer7). Specifically, atmospheric pCO2 levels can be expressed as
where δ13Cs, δ13Cr, and δ13Ca refer to the carbon isotopic compositions of total soil CO2, soil-respired CO2, and atmospheric CO2, respectively, and S(z) is the soil-respired CO2 concentration at soil depth z during the time of carbonate precipitation. Generally, the soil δ13Cs is calculated from δ13Cc (the carbon isotopic composition of pedogenic carbonate) using a temperature-dependent fractionation factor8; the soil-respired δ13Cr is approximated by δ13C value of coeval soil organic matter (SOM) preserved in the same paleosol strata9; and the carbon isotopic composition of atmospheric CO2 (δ13Ca) can be estimated from marine carbonate records10. This approach has been extensively applied to pedogenic carbonates worldwide11 to reconstruct pCO2 over the geological past. Approaches to determine the carbon isotopic terms (δ13Cs, δ13Cr, and δ13Ca) have been well established. However, significant uncertainties still remain in this paleosol CO2 barometer, which is mainly sourced from the S(z) term that describes soil respiration12.
S(z) has been difficult to constrain. Early studies11 commonly treated S(z) as a constant of 5000 ppm based on limited modern observations13. However, accumulating evidence over the last decade has shown that S(z) is highly variable both spatially and temporally14,15. Studies of Holocene calcareous soils demonstrated that pedogenic carbonate precipitates under warm, dry climatic conditions, when soil productivity, and S(z) are much lower than previously assumed14. Besides, among different soil types and soil moisture regimes, S(z) can vary by up to two orders of magnitudes16. The extensive variability of S(z) across different climatic conditions and soil types leads to large uncertainties of the paleosol-based method, especially for the late Cenozoic when pCO2 is low with small variations17. Instead of treating S(z) as a constant, recent works took into account of the variability of S(z) either by establishing empirical models equating S(z) with other climatic parameters such as mean annual precipitation (MAP)18, or by defining soil order-specific ranges15. Although a major step forward, both approaches have caveats. Estimates of S(z) using MAP proxies such as CIA-K (chemical index of alteration without potassium)18 or DTC (depth to carbonate nodular horizon)19, are empirically developed based on modern soil systems, but have not been validated for applications in paleosols20. S(z) values of different soil types, for example, the aridisols, still vary from 500 to 2500 ppm15, which would contribute to a five-fold spread in estimated pCO2. Importantly, the calculated pCO2 scales proportionately with S(z) (Eq. (1)), making it a vital factor for the success of paleosol-derived CO2 estimates.
In this study, we seek to improve the paleosol CO2 barometer by providing more robust constraints on S(z). To achieve this, we focus on the finely disseminated carbonates (FDC) in bulk paleosols on the Chinese Loess Plateau (CLP). Field observations and scanning electronic microscopy (SEM) imaging together demonstrate a shallow formation depth of FDC (soil Bt/Bw horizon)21. Further, a suite of geochemical analyses are used to test the pedogenic origin of these carbonates, as well as the potential of diagenetic alterations. Rather than assuming a constant S(z) for all samples, we explore the possibility of sample-specific S(z) values by employing soil magnetic susceptibility (MS) as a proxy for S(z). With this refined method and new data, we intend to provide a better assessment of the interglacial pCO2 for the early Pleistocene epoch from a terrestrial perspective.
Geological setting and sampling
The accumulation of eolian material on the CLP initiated during the early Miocene22. In the Quaternary loess–paleosol sequence, paleosol units formed during interglacial episodes were characterized by slower eolian dust deposition, strengthened summer monsoonal rainfall, and enhanced pedogenesis relative to the glacials23. Large seasonal changes in precipitation and evaporation contribute to the wide occurrence of pedogenic carbonates across the CLP. Unlike the more humid southeastern CLP (e.g. typical sites including Lantian, Baoji), where extensive leaching completely decalcified the paleosols, or the more arid northwestern CLP (e.g. Huanxian, Jingyuan), where large amount of detrital carbonates remained due to insufficient rainfall24, our sampling location, the Luochuan section (35.76°N, 109.42°E) located in the central CLP (Supplementary Fig. 1), is characterized by the appropriate level of pedogenesis. The detrital carbonates are mostly absent in paleosol samples, whereas authigenic carbonates are still preserved (Supplementary Fig. 2). Before sampling, we trenched the soil profile (>1 m deep) to avoid contamination of regolith, and monitored the MS values of bulk paleosols, which were compared to published data25. Each sample was collected within a 10 cm interval. Paleosol samples used in this study mainly occur within the soil Bt/Bw horizons, characterized by subangular blocky structure with clay coatings attached on structural faces, and a 5–7.5 YR Munsell color.
Finely disseminated carbonates
In the field, the carbonates in our targeted paleosol samples have identifiable pedofeatures including finely disseminated cements filling the soil matrix, and carbonate hypocoatings (i.e. pseudomycelia) lining pores and tubules, which can be categorized as Stage 1 pedogenic carbonate26. Therefore, we term this carbonate fraction as FDC. SEM imaging further reveals that our sampled FDC are mainly composed of 5–10 μm-long needle fiber calcite (NFC), and clustered nanoscale calcite nanofibers (Fig. 1a–d). The SEM results are consistent with previous findings that NFC is commonly associated with smaller carbonate fibers such as nanofibers27, indicating similar formation conditions and a pedogenic origin. Importantly, NFC mostly appears between the humic horizon (O horizon) and subsurface C zone and vanishes with depth28. The location of NFC matches our field observations, which indicate the occurrence of FDC within the relatively shallow soil Bt/Bw horizon in comparison to the nodule-bearing Bk horizon. The origin of NFC is tied to both organic (fungal biomineralization) and inorganic activities (physicochemical precipitation)29,30. Whichever the case, it appears that the stable isotopic compositions (δ13C and δ18O) of NFC are indistinguishable from coeval calcite cements (rhombohedral calcite crystals)31, making bulk measurements of FDC well representative of all encapsulated calcite phases.
Incomplete dissolution of the detrital carbonate components (calcite and dolomite) from parent material of the loess (e.g. eolian dust) would bias the δ13C of the bulk soil carbonates. However, they appear to only impose very minor influence on our samples because we selected samples without the presence of any dolomite for subsequent analyses, as measured by the Fourier transform infrared spectrophotometry that is highly sensitive to carbonates24. Dolomite has a slower dissolution rate than calcite, and the final disappearance of detrital dolomite ensures the complete dissolution of detrital carbonates24. Further, we also measured trace elements of the FDC fractions in our paleosol samples. Previous work has shown that the concentrations of trace elements (e.g. Mn, Mg, and Sr) in pedogenic carbonates from the CLP are considerably lower than those of detrital carbonates derived from marine carbonate strata in source regions32, and are highly correlated with rainfall intensity33. In this study, we identified that the Sr/Ca and Mg/Ca ratios of the FDC fractions range from 0.72 to 1.48 mmol/mol (mean = 0.98 ± 0.31 mmol/mol) and 36–140 mmol/mol (mean = 81 ± 30 mmol/mol), respectively, both of which are generally consistent with those of microcodium (typical authigenic carbonate in paleosols) in Holocene soils on the CLP (Sr/Ca = 1.08 ± 0.68 mmol/mol, Mg/Ca = 48 ± 29 mmol/mol) (Fig. 1f)33. The Mn/Ca and Mg/Ca ratios of the FDC fractions are significantly lower than the carbonate samples from potential source regions of the loess— the deserts in Northern China (Fig. 1e)32, providing additional evidence for the pedogenic origin of our bulk paleosols carbonates.
Diagenetic alterations (i.e. the dissolution and reprecipitation of fine-grained carbonates) could also affect δ13C and other geochemical signatures. However, we expect this process to have minimal influence on our carbonate samples for two reasons. Firstly, the long-term trend of δ13C derived from the FDC fractions of our paleosol samples are almost identical with that determined from δ13C of coeval calcite nodules throughout the Pleistocene, although the nodule record has a much lower resolution (Supplementary Fig. 3). Calcite nodules are usually considered to be buffered against diagenesis11,18. Notably, the Pliocene paleosol formations in the CLP also show indistinguishable δ13C and δ18O values from mm-scale micrites to massive carbonate horizons34, suggesting that the FDC could potentially be used to reconstruct pCO2 beyond the Pleistocene. Secondly, numerous studies of paleosol carbonates from the CLP suggest that their geochemical signals are pristine and record near-surface conditions. For instance, trace metal compositions of fine-grained pedogenic carbonates from loess–paleosol sections in the CLP appear to preserve local precipitation signals33 and show high-frequency variations on orbital timescales35.
Based on field observations, micromorphology, and geochemical characteristics, we conclude that the FDC fractions used in this study are of a pedogenic origin with minimal diagenetic alteration, thus suitable for paleosol-based pCO2 reconstructions.
Rearranging Eq. (1) and we obtain
which provides a mathematical solution for S(z). Carbonate and SOM were measured for stable C isotopes to obtain δ13Cs, and δ13Cr (see the “Methods” section). δ13Ca was obtained from marine carbonate δ13C10. Atmospheric pCO2 over the last 800 ky were derived from the ice core pCO2 record36. Together they were used to compute S(z) of the Luochuan section over the last 800 ky. To estimate the uncertainties of the back-calculated S(z), we adopted Monte Carlo random sampling simulations to propagate errors from all input parameters (Supplementary Note 1). In brief, for each sample, we randomly sampled each parameter in Eq. (2) within its error range for 10,000 times and calculated a corresponding S(z) population. We report S(z) as the median values of the results from the Monte Carlo simulations, and define the associated uncertainties using the 16th and 84th percentiles of the simulated S(z) population (corresponding to the median value and the ±1σ error range in a standard Gaussian distribution).
When pedogenic carbonate precipitates deep in the soil profile where soil-respired CO2 dominates over atmospheric CO2, back-calculated S(z) are inherently associated with sizable errors7. We therefore adopted the concept of an R factor, defined as the ratio between [CO2]atm and S(z) (R = (δ13Cs − 1.0044 × δ13Cr − 4.4)/(δ13Ca − δ13Cs)), as a screening criterion7. When atmospheric CO2 constitute a minor portion of soil CO2 (R < 0.3 according to ref. 7), the samples are thought to be dominated by soil-respired CO2 thus discarded for subsequent analyses. Twenty-two paleosol samples passed this criterion, representing 78% of all the samples analyzed for S(z). The calculated median S(z) levels over the last 800 ky show variations from 356 to 815 ppm, with uncertainties on average of +96/−75 ppm (Fig. 2a).
MS as a proxy for S(z)
Soil-respired CO2 comes from two major sources—the respiration of autotrophs, such as plant roots, and heterotrophs, such as the soil microbes mediating the oxidation of SOM. Studies of modern soils have shown that S(z) as a measure of soil productivity, is strongly correlated to climate parameters, such as temperature, precipitation, and evapotranspiration37. Notably, among carbonate-bearing soils in semi-arid to arid regions, such as the CLP, S(z) is mainly controlled by precipitation18,37. To quantitatively constrain S(z), here we explore a potential proxy sensitive to precipitation changes—soil magnetic susceptibility (MS).
The MS of bulk soil samples is predominantly controlled by the presence of ultrafine magnetite38,39, which is efficiently produced in situ under well-drained soils with alternative wet (Fe2+ produced) and dry (Fe2+/Fe3+ oxide precipitated) cycles. The ultrafine ferromagnetic grains are either directly produced by magnetotactic bacteria, or formed by inorganic precipitation, mediated by the production of Fe2+ through iron-reducing bacteria40. Similarly, modest precipitation increase would enhance microbial activities, the formation of magnetic iron oxides and consequently soil MS, but MS decreases under excessive rainfall (MAP > 1000 mm) as the production of ferrimagnet ceases41. MAP > 1000 mm probably never occurred in the Pleistocene history of the central to northern part of the CLP42. As a result, MS is regarded as a sensitive paleoclimate proxy of pedogenesis intensity and paleorainfall40, and has been widely used to address the evolution history of the East Asian summer monsoon23,43.
Intensified precipitation would facilitate the formation of magnetic iron oxides (i.e. MS), and increase soil productivity and S(z). Because rainfall regulates soil MS and S(z) in a similar manner on the CLP, these two parameters are expected to be correlated. Indeed, when the two parameters from the Luochuan samples covering the last 800 ky were plotted against each other, we observe a statistically significant correlation (Fig. 2a):
The fitting is done using the least-squares linear regression model, and the uncertainties on the slope and intercept represent 1σ standard errors. Extrapolating this relationship to the entire Pleistocene will enable sample-specific S(z) using measured MS, and consequently the calculation of pCO2 from paleosols (MS–S(z) approach). By providing new constraints on S(z), this MS–S(z) approach potentially improves the paleosol method for reconstructing pCO2.
To validate the MS–S(z) approach, we next recalculated the S(z) of our 800-ky paleosol samples using the MS–S(z) approach, and compare the derived pCO2 to those documented in ice cores. Because the determination of the MS–S(z) relationship relied on the ice core CO2 record, to avoid circular reasoning, we adopted a resampling technique. Specifically, the 22 samples were divided into two subsets: a training sample group and a test sample group. A MS–S(z) regression was established from the training group, and used to estimate S(z) for the test group, the resulting pCO2 of which were then compared to the ice core data. For a given training sample number n, a bootstrap sampling of 1,000,000 times was performed (each time, we obtained 22 − n pCO2 values). We also varied the sample numbers in the training group from n = 10 to n = 21. During each run, the mean relative difference χ between the calculated pCO2 and those from the ice core data was calculated:
The statistical distributions of χ (Fig. 2b and Supplementary Fig. 4) show that, across different training sample number n, χ is clustered around 0 with >70% of the data points falling within ± 10% difference. This consistent pattern among different n values strongly supports our MS–S(z) approach for pCO2 reconstruction over the last 800 ky.
Reconstructing early Pleistocene pCO2
The refined soil carbonate-pCO2 approach was also applied to the samples from the lower section of the Luochuan profile spanning the early Pleistocene, beyond the available ice core records. Measured MS and stable carbon isotopes for those early Pleistocene samples were used to calculate S(z) and pCO2, assuming that the MS–S(z) relationship remains (Eq. (3)). We calculated the uncertainties on pCO2 by propagating the uncertainties associated with the analyses of all input parameters and the MS–S(z) regression equation using PBUQ, a published MatLab-based program that adopts Monte Carlo random sampling simulations for uncertainty analysis7. We report the median values of the calculated pCO2, and define the uncertainties as the 16th and 84th percentiles (as ±1σ), and the 2.5th and 97.5th percentiles (as ±2σ) of pCO2 distributions from Monte Carlo simulations (see the “Methods” section).
The calculated S(z) during ~2.6–0.8 Ma vary between 276 and 644 ppm, with errors (1σ) ranging from 76 to 113 ppm (Fig. 3c). The R values (pCO2/S(z)) are generally higher (>0.3) during the early Pleistocene, suggesting that these samples are suitable for pCO2 reconstructions. This newly established interglacial pCO2 records show variations from 183 to 292 ppm (averaged median pCO2 levels for each interglacial episode) during 2.6–0.9 Ma (Fig. 3d). Except for some data points centered around the Pliocene–Pleistocene boundary (2.6–2.5 Ma) and the MPT showing relatively higher pCO2 exceeding 300 ppm, our paleosol-CO2 estimates document overall low early Pleistocene pCO2 levels similar to those over the last 800 ky (Fig. 3d). The reconstructed pCO2 values have an 1σ error range of +92/−82 ppm when averaging the errors for all individual results.
To evaluate the role pCO2 played for the MPT, we performed a detailed comparison of MPT–pCO2 with those before and after the MPT (i.e. pre-MPT and post-MPT), the durations of which were considered to be 400 ky equivalent to the MPT itself (i.e. 0.8–0.4 Ma for post-MPT and 1.6–1.2 Ma for pre-MPT). Our paleosol-based CO2 reconstructions provide 16 estimates during the MPT and 21 pre-MPT. pCO2 estimates during the MPT and pre-MPT were then converted into factor changes in CO2 by normalizing pCO2 to the mean post-MPT pCO2 from ice cores, since our paleosol–CO2 estimates are indistinguishable from ice core data (Fig. 2b and Supplementary Fig. 4). We calculated the probability density functions (PDFs) and cumulative distribution functions (CDFs) of the factor changes in CO2 among different time periods (i.e. MPT/pre-MPT, MPT/post-MPT, pre-MPT/post-MPT) (Supplementary Note 2). As indicated by both absolute values and the factor changes, pCO2 level during the MPT (mean = 269 ± 38 ppm, 1σ = +105/−94 ppm) was ~15% higher than that of the post-MPT (mean = 231 ± 37 ppm), and ~20% higher than that of the pre-MPT (mean = 217 ± 25 ppm, 1σ = +73/−67 ppm) (Fig. 4a). Results from the PDFs and CDFs also confirm this distribution (Fig. 4b, c).
The foundation of the refined paleosol-based pCO2 estimates lies in the premise that soil MS can be used to constrain S(z), with the rationale that on the CLP, both parameters are controlled by monsoonal precipitation. However, soil residence time, or the duration of pedogenesis before they were deeply buried by the newly arrived eolian material, could potentially affect MS, thus hampering the application of our MS–S(z) approach. However, multiple lines of evidence suggest that since soil formation, soil MS quickly reaches a near-steady-state equilibrium status, insensitive to the duration of pedogenesis. For instance, the MS of modern surface soils across the CLP region (30–200)44 are equivalent to those of the Pleistocene paleosols (60–220) from this study, even though the modern soils have undergone much shorter periods of pedogenesis.
Changes of the accumulation rate of dust supply could also modify soil properties. However, in the central CLP region (e.g. Luochuan in this study), the mean mass accumulation rate of loess remained relatively constant (ca. 5–8 g m2 yr−1) without discernable trend during the interglacial cycles over the last 2.6 Ma45. As a consequence, we render that the observed correlation between MS and S(z) over the last 800 ky can be applied to early Pleistocene paleosols.
It is noteworthy that interglacial MS levels during the early Pleistocene (99 ± 28) are generally lower than those during the last 800 ky (154 ± 28), and most of the MS values (78 ± 11) of our 1.7–1.5 Ma samples fall below the MS range (99–227) over the last 800 ky. This translates to low S(z), low soil productivity, weak pedogenesis, and perhaps drier climate during the early Pleistocene, which is consistent with our current understanding of the early Pleistocene climate on the CLP42,46. For instance, Fe minerals found in the CLP sequences are sensitive to climate changes, as high temperatures and limited seasonal rainfall would favor the formation of hematite over goethite. The hematite/goethite ratio of Luochuan section demonstrates a long-term, stepwise decreasing trend from 0.25 to 0.3, since the Pliocene/Pleistocene boundary, to as low as 0.2 towards the late Pleistocene, indicating reduced monsoonal precipitation during the early Pleistocene47.
Previous estimates of the early Pleistocene pCO2 mostly come from the applications of geochemical proxies to marine sediments (e.g. alkenone and boron approaches)48,49,50,51,52. Although results from both boron and alkenone-based proxies suggest an overall decreasing trend since the early Pleistocene, discrepancies remain among individual records (Fig. 5). For instance, the composite view from two boron isotope records48,49 indicates a sudden decline of pCO2 at ~2.2 Ma, while the alkenone proxy suggests a gradual decline since ~2.5 Ma. Two alkenone-based results17,50, however, show early Pleistocene pCO2 values higher than 300 ppm, significantly elevated from the late Pleistocene levels recorded by ice cores. Both alkenone and boron proxies rely on certain assumptions, which could be invalidated by local physical, chemical, and biological processes53. For example, marine-based pCO2 reconstructions assume that an air–sea equilibrium of CO2 is maintained for the entire studied interval, which does not necessarily always hold. In addition, the boron method requires the knowledge of a second carbonate system such as alkalinity or dissolved inorganic carbon54. Similarly, the alkenone method requires constraints on the physiological conditions of alkenone-producing haptophyte algae55. Curiously, the recently studied blue ice which are outcrops of old ice from Antarctica show that pCO2 remained <300 ppm for at least 1 million years56 and possibly 2.7 million years57, contradicting to some of the boron-based and alkenone-based results (Fig. 5b, c). In this respect, terrestrial archives free of the air–sea disequilibrium of CO2 problem could weigh into the absolute values of Pleistocene pCO2 problem.
Our terrestrial-based record shows that interglacial pCO2 levels during 2.6–0.8 Ma varied between 183 and 292 ppm (averaged for each interglacial), with the lower pCO2 levels within this range often associated with samples collected close to the paleosol–loess (i.e. interglacial–glacial) transitions. These pCO2 estimates are similar to the ice core pCO2 record of the last 800 ky (Fig. 5d), and consistent with the blue ice records which show <300 ppm pCO256.
Coupled general circulation model/ice sheet model have suggested that, the pCO2 has to drop below the threshold of 280 ppm to induce major Northern Hemisphere glaciations (NHG)58. This is confirmed by this paleosol-based record, as well as a recently published high-resolution δ11B-pCO2 record48. However, some of the earlier estimates using marine archives showed >400 ppm of pCO2 estimates prior to ca. 2.3 Ma48,50 (Fig. 5b, c). A recent study has identified that the traditional alkenone method tends to overestimate Pleistocene CO2, which can be explained by the physiological parameter b used that are on average, too large59.
The gradual decline of pCO2 over the last 3.0 Ma has been hypothesized to trigger the MPT transition60,61. Recently published high-resolution pCO2 record using δ11B proxy62 documents an overall higher CO2 level (241 ± 21 ppm) during the early part of the MPT (1.25–1.08 Ma) than that during 0.26–0 Ma (203 ± 14 ppm) (Fig. 5c). Our paleosol-based pCO2 values also demonstrate a statistically significant decline of ~40 ppm from the MPT to the post-MPT period (Fig. 4a). However, the pCO2 record presented in this study shows that the MPT itself was accompanied by a CO2 rise of ~50 ppm (Fig. 4a). Calculation of factor changes in CO2 among three time periods (i.e. pre-MPT, MPT, and post-MPT) also show a significant CO2 peak during the MPT, and no apparent CO2 difference before and after the MPT (Fig. 4). This analysis indicates that the low CO2 condition was already established long before the MPT. As a consequence, our results do not support the supposition that the decline of pCO2 lead to the onset of the MPT.
The chronological framework of loess–paleosol sequences in Luochuan are based on the paleomagnetic reversal sequences, with the detailed information described in previous studies63. The Brunhes–Matuyama reversal occurs among the transition of L8 (loess unit 8) and S8 (paleosol unit 8). The Jaramillo subchron is defined between the upper part of L10 and the base of S11, while the Olduvai subchron lies between the middle part of L25 and the lower part of S26. A basal age of ∼2.6 Ma is estimated for the Chinese loess deposits, based on the Matuyama/Gauss magnetic reversal occurring in the oldest loess unit, L33. The stratigraphy of loess–paleosol sequences can be further delineated by MS data, which was measured through a Bartington MS system (5% accuracy), with higher bulk MS occurring in paleosols and lower values in loess layers. The good correlation between MS of loess–paleosol sequences and glacial–interglacial stages recorded by benthic δ18O (Supplementary Fig. 1) further supports the robustness of this chronology. To be able to directly compare between paleosol-derived and marine-derived pCO2 records, we tuned the MS data to the benthic δ18O stack LR0464. Specifically, the top and basal age of each paleosol unit is assigned by the beginning and end of the corresponding interglacial episode (defined by the higher 50 percentiles of δ18O values), and the ages within a single unit were calculated through interpolation. Because of the shallow depth of origin of the pedogenic carbonates, we did not apply any offset between their ages and the ages of paleosol layers where they were sampled from.
δ13C and trace element analyses
Calcite and dolomite contents of bulk soil samples were measured through Fourier transform infrared spectrophotometry, following procedures described in ref. 24. To ensure that our samples were free of detrital carbonates, only paleosols without dolomite were applied for subsequent analyses24. In order to obtain δ13Cr and δ13Cs for pCO2 calculation, the δ13C values of pedogenic carbonates in bulk soil samples (i.e. FDC), and co-occurring SOM were measured. For carbonate isotope analyses, bulk soil samples were treated with 10% H2O2, the remaining of which were then oven-dried, crushed, and grinded into powder for homogenization. Samples were then analyzed on a ThermoFinnigan MAT 253 isotope ratio mass spectrometer using a Kiel IV carbonate device (75 °C reaction in 100% H3PO4). For organic carbon isotope analyses, bulk soil samples were reacted with 1 M HCl to ensure complete dissolution of carbonates, and then ultrasonically rinsed with deionized water for multiple times until pH reached neutral. The oven-dried residues were grinded into powder, loaded into tin capsules and analyzed on the ThermoFinnigan MAT 253 isotope ratio mass spectrometer with a Costech elemental analyzer attached. Both carbonate and organic carbon isotopic results are reported in permil (‰) notation relative to the Vienna Pee Dee Belemnite (VPDB) standard with a precision better than ±0.2‰ from duplicate analyses. Multiple samples (>3) from each paleosol unit were measured, with the averaged standard deviations for each paleosol unit about 0.47‰ (carbonate) and 0.43‰ (SOM). For trace element analysis of carbonate fractions, bulk samples were dissolved in 0.2 M acetic acid following the method described in ref. 65. Trace element concentrations of dissolved solutions were then measured on an ICP-OES 6300. Precisions are better than 0.3% for Mn/Ca, Mg/Ca, and Sr/Ca following ratio calibration method described in ref. 33.
Input parameters and error propagation
In this work, input parameters related to the paleobarometer equation were either directly measured or estimated. δ13Cs values can be solved by δ13Cc through a temperature-dependent fractionation equation8. Previous work based on Pliocene pedogenic carbonates from the CLP66 revealed that the formation temperature of pedogenic carbonates is 1−2 °C lower than modern day summer air temperature (from June to September), and since Pliocene was globally warmer than Pleistocene67,68, the formation temperature of pedogenic carbonates during the Pleistocene were probably not higher than the Pliocene. Therefore, we used a correction of −1.5 °C for the modern summer (JJAS) air temperature (18.4 °C for Luochuan), to represent the formation temperature of our pedogenic carbonates throughout the study interval. Uncertainty associated with temperature was set to ±3 °C. Previous investigations have determined minor δ13C fractionation between soil-respired CO2 and soil organic matter (SOM)9, therefore δ13Cr values were approximated through δ13C of SOM from the same paleosol layer. However, carbon isotope fractionation occurs during decomposition of SOM, which could enrich the δ13C of bulk paleosol organic matter69. Therefore, we applied a universal correction of −1 ± 0.5‰ for our δ13CSOM, following the difference of δ13C values between the A and B horizon in an archived soil70. Errors associated with the δ13Cs and δ13Cr were assigned based on the standard deviations of measured δ13Cc and δ13CSOM (n > 3) within the same paleosol unit. δ13Ca values were derived from measured δ13C values of contemporaneous marine benthic foraminifera carbonates10. To calculate pCO2 and propagate errors associated with input variables, we used the MatLab-based PBUQ program7. PBUQ calculates probability density functions for each variable based on input parameters and associated uncertainties (assumed to be normal distribution), which are generated using 10,000 iterations (Monte Carlo simulations). This program yields median R and pCO2 values with error bars extending to the 16th and 84th percentiles.
All stable carbon isotope and magnetic susceptibility data from the Luochuan section of the Chinese Loess Plateau, as well as the calculated S(z) and pCO2 are attached as a Supplementary Data file.
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This work was funded by National Natural Science Foundation of China (41773118 and 41230526 to J.J.) and the program A for Outstanding Ph.D. candidate of Nanjing University (to J.D.).
The authors have no competing interests to declare.
Peer review information Nature Communications thanks Daniel O Breecker, Gregory Retallack and other, anonymous, reviewers for their contributions to the peer review of this work. Peer review reports are available.
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Da, J., Zhang, Y.G., Li, G. et al. Low CO2 levels of the entire Pleistocene epoch. Nat Commun 10, 4342 (2019). https://doi.org/10.1038/s41467-019-12357-5
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