No apparent state-dependency of equilibrium climate sensitivity between the Pleistocene glacial and interglacial climate states

Abstract

Quantifying climate sensitivity is essential for future climate projections, yet it varies with major Earth system changes. We present a glacial CO₂ reconstruction using paleosols from the Chinese Loess Plateau, covering 2580 to 800 thousand years ago. A stepwise decline in glacial CO₂ levels from ~300 ppm to <200 ppm is observed. Our paleosol-based CO₂ estimates support the key role of atmospheric CO₂ in driving major climate transitions during the Pleistocene, such as the long-term global cooling and the amplification of the glacial cycles. Based on compiled glacial and interglacial CO₂ records, Earth system sensitivity, defined as the global temperature change for a doubling of CO₂ once the whole Earth system has reached equilibrium, is estimated to be ~6.2–7.4 K (3.2–12.0 K, 95% confidence). Equilibrium climate sensitivity, after accounting for the different efficacy between ice-sheet and CO₂ forcing and other slow feedbacks, is estimated to be 3.3 K (2.1–6.3 K, 95% confidence) and 3.7 K (1.7–6.3 K, 95% confidence), respectively. The lack of a significant difference between these values suggests no apparent state-dependency of climate sensitivity between glacial and interglacial climate states.

Introduction

Equilibrium climate sensitivity (ECS) refers to the global mean surface temperature response to changes in radiative forcing caused by a doubling of atmospheric CO₂ concentration when the responses to fast feedbacks reach equilibrium¹. ECS is a useful measure of the impacts of greenhouse gas emissions on global temperatures and provides a critical reference for future policymaking regarding climate mitigation². Paleoclimate studies offer a “deep-time” perspective on ECS as they capture long-term Earth system responses under large ranges of CO₂ forcing, which helps evaluate the feedback processes and improve climate models³. The Pleistocene epoch experienced long-term cooling marked by the expansion of bipolar ice sheets⁴ and the amplification of glacial cycles from 400 ky during 2580–1250 thousand years ago (ka) (the “40k world”) to 100 ky since 700 ka (the “100k world”)^5,6, with this climatic transition often referred to as the Mid-Pleistocene Transition (MPT)⁶. As such, the Pleistocene represents a natural experiment from which empirical estimates of ECS can be derived^7,8. However, studies of the early Pleistocene ECS are rare, with high uncertainty⁸, which largely results from the lack of high-resolution, high-fidelity CO₂ records.

Early Pleistocene CO₂ levels are mainly estimated by proxies from a variety of geological archives^9,10,11. Recent work on the Antarctic blue ice managed to extend direct CO₂ measurements to ~3000 ka^12,13 (Fig. 1b). Nonetheless, the blue-ice data provide limited snapshots of the early Pleistocene, which may fail to capture overall CO₂ variations^12,13. The δ¹¹B values of planktic foraminifera and δ¹³C values of algal biomarkers such as alkenones provide extensive Pleistocene CO₂ estimates, yet none of the existing CO₂ records cover the entire Pleistocene with ample resolution^{9,14,15,16,17}. Moreover, due to various limitations related to each proxy (e.g., biological “vital” effects and post-burial diagenesis), it is necessary to reconstruct paleo-CO₂ from a multi-proxy perspective¹⁸. Notably, since ~2000 ka, the available CO₂ data from blue-ice measurements¹² and proxy-based estimates (δ¹¹B and paleosols)^9,10,17 show a constant maximum CO₂ of 280–300 ppm (Fig. 1b and Supplementary Fig. S1), in contrast to the long-term cooling as suggested by marine benthic δ¹⁸O^19,20 (Fig. 1a). Our previous work based on the paleosols from the Chinese Loess Plateau also suggests CO₂ was nearly constant among Pleistocene interglacials¹⁰. Although a long-term glacial CO₂ record is absent, studies on the MPT suggest that glacial CO₂ dropped by 24–38 ppm from the 40 k to the 100 k world, which might have played a key role in the long-term global cooling^9,12,17,21, a supposition supported by recent conceptual modeling, which calculated changes in global ice-sheet volume in response to different forcing scenarios²². This has motivated us to establish a Pleistocene glacial CO₂ record, aiming to elucidate the relationship between long-term CO₂ evolution and changes in the climate system.

Fig. 1: Pleistocene climate and atmospheric CO₂ levels.

a Benthic-δ¹⁸O stack¹⁹. Shaded areas correspond to glacial periods. b Ice-core CO₂ record over the past 800 ky⁷⁸ and early Pleistocene blue-ice CO₂ snapshots (circles)¹². c Glacial paleosol-based CO₂ estimates from this study, compared with the ice-core record. Error bars denote 1σ errors from Monte Carlo simulations. Blue curve denotes the LOESS smoothed curve with a span of 0.5 (50% of all the data that are nearest to a given age were included in the local regression fit). Horizontal dashed lines highlight the maximum and minimum CO₂ from the Antarctic ice.

The paleosol-CO₂ proxy is a key method for reconstructing paleo-CO₂ from the terrestrial perspective²³. The carbon isotope composition (δ¹³C) of pedogenic carbonate records the δ¹³C of soil CO₂ that consists of two endmembers with distinct δ¹³C signals—CO₂ from soil respiration and atmospheric CO₂²⁴. Pedogenic carbonate thus documents the concentration of atmospheric CO₂, provided that several input parameters can be constrained^25,26 (Materials and Methods). However, soil-respired CO₂ concentration at soil depth z of pedogenic carbonate formation (S(z)), a key variable that underpins this methodology, remains poorly constrained and introduces considerable uncertainty to the paleosol-CO₂ proxy²⁶. Moreover, due to the lack of continuous occurrence of paleosols in sediment strata as well as precise dating methods, the paleosol-CO₂ method also suffers from low time resolution.

In this study, we leverage the continuous, well-dated paleosols from the Chinese Loess Plateau (CLP), where eolian deposits experienced soil development under the influence of the East Asian summer monsoon²⁷. The Quaternary deposits on the CLP, known as the loess-paleosol sequences, are characterized by alternating light yellow ′loess′ units (Entisols, poorly developed paleosols) and dark brown ′paleosol′ units (Aridisols/Mollisols, stronger pedogenesis) formed during glacial and interglacial episodes, respectively. The chronological framework of the loess-paleosol sequences is built on magnetostratigraphy and other direct dating methods²⁷, enabling widespread comparison with other high-resolution archives such as marine sediments and ice cores²⁸. We reconstructed CO₂ levels during glacial periods (as identified by the deposition of weakly pedogenically modified loess, which have been correlated with Marine Isotope Stage glacials) of the entire early Pleistocene (2580–800 ka), using paleosols collected from two sections, Fuxian and Zhaojiachuan, situated in the central CLP (Materials and Methods, Supplementary Fig. S2). Owing to the nearly continuous eolian deposition and seasonal wet-dry cycles, pedogenic carbonates grew throughout the CLP eolian deposits, making them excellent materials for continuous CO₂ reconstruction.

Our previous work reconstructed interglacial CO₂ levels using finely disseminated calcites from the paleosol units¹⁰. In this study, we overcame several principal uncertainties (i.e., detrital contamination, ages, magnitude of S(z)) that are particularly relevant to weakly developed paleosols within CLP loess units to reconstruct glacial CO₂ levels. The newly reported glacial CO₂ was used in tandem with published CO₂ records and various global climate records to assess climate sensitivity across the Pleistocene epoch.

Results and discussion

Pedogenic carbonates documenting glacial CO₂ levels

Before using soil carbonates for glacial-CO₂ reconstructions, two prerequisites need to be met: 1) ensuring that these carbonates were formed during pedogenesis and are free of detrital (originating from soil parent materials) carbonates, and 2) confirming the absence of significant illuviation process, which would cause substantial offsets between the depositional ages of loess and the formation ages of pedogenic carbonates.

The parent material of the CLP paleosols, composed of eolian dust from inland Asia, contains detrital carbonates such as dolomite and calcite²⁹, the δ¹³C values of which are distinct from pedogenic carbonates³⁰. During interglacial periods, strong pedogenesis dissolved all the detrital carbonates in some paleosol units³⁰. During glacial periods, pedogenesis was weaker and therefore all the loess units contain certain amounts of detrital carbonates³⁰. To ensure our glacial period carbonate samples are pedogenic and not detrital, we isolated carbonate in the clay-sized fractions (<2 μm) from bulk paleosols (Materials and Methods). Scanning electron microscopy imaging confirms that the clay-sized fractions are predominantly nanoscale needle fiber calcite (NFC, Supplementary Fig. S3)–a typical form of pedogenic carbonate³¹. Recent efforts have focused on understanding the formation and geochemistry of NFC in these paleosols, as well as utilizing them for paleoclimate reconstructions^10,32. Radiocarbon ages of clay-sized carbonates formed during the last glacial period closely align with those of coeval soil organic matter and are younger than the depositional ages of the loess from corresponding stratigraphic levels, as expected for pedogenic materials (Materials and Methods, Supplementary Fig. S4), suggesting minimal contribution from radiocarbon-dead detrital carbonates.

During interglacial episodes, increased rainfall promotes intensive leaching of carbonate minerals and deep carbonate accumulation that could penetrate the underlying glacial units¹⁰. Therefore, the age determination of pedogenic carbonates in the upper part of the glacial units becomes complicated. To circumvent this issue, our samples were taken exclusively from the lower sections of the glacial (loess) units. Because our carbonate samples are dominated by NFC that grows close to the soil-air interface³³, it is unlikely that they were formed during interglacial periods. Moreover, the radiocarbon ages of these clay-sized carbonates from the top of the L1 glacial unit, where the accumulation of younger carbonates during the Holocene is likely most problematic, indicate they are at most 10-ky younger than the depositional ages of the loess in which they reside (Supplementary Fig. S4), suggesting that the clay-sized carbonates lower in the glacial units (and therefore presumably older) were formed during glacial periods. Taken together, all evidence supports our carbonate samples in the clay-sized fractions as valuable archives for documenting glacial paleoenvironments, including atmospheric CO₂ levels. Notably, since we specifically sampled the lower part of the glacial units, our records are likely biased towards the beginning of glacials. Nonetheless, because early Pleistocene glacial cycles do not have the “saw-tooth” pattern evident in late Pleistocene, sampling the bottom half of the glacial units should provide a good estimate of mean glacial conditions.

δ¹⁸O_c as a proxy for glacial S(z)

The accuracy and precision of the paleosol-CO₂ method hinge on the constraints on S(z)²⁶. Determining S(z) in paleosols has been challenging due to its high seasonal and spatial variations³⁴, which introduces considerable uncertainty to the resulting CO₂ estimates²⁶. In our previous work on interglacial CO₂, S(z) was estimated through soil magnetic susceptibility, as both parameters respond to monsoonal rainfall¹⁰. However, this method loses its sensitivity in less-weathered glacial loess units due to a relatively high rainfall threshold for magnetite growth and increased interference with detrital magnetite from the parent material³⁵.

We therefore investigated the δ¹⁸O values of the clay-sized pedogenic carbonates (δ¹⁸O_c) as a proxy for glacial S(z). A negative relationship between δ¹⁸O_c and S(z) is expected from a process perspective because they are influenced by similar factors. Soil water δ¹⁸O values (the principal control on δ¹⁸O_c) inherit rainfall δ¹⁸O values, which in monsoon climates such as the one studied here, tend to decrease as rainfall amount increases³⁶. Conversely, S(z) values increase with rainfall amount because they increase with soil respiration rate and the depth of carbonate accumulation, both of which increase with rainfall^37,38. Thus, S(z) should increase as δ¹⁸O_c decreases. Moreover, we expect that this negative relationship is accentuated by gas transport affecting both evaporation and the escape of respired CO₂ from soils. Evaporation and respired CO₂ escape from soil by net diffusion from the soil pore spaces to the atmosphere. When pathways for gas diffusion are restricted, the gases are retained in the soil, minimizing evaporation and elevating S(z). Because evaporation increases the δ¹⁸O value of residual soil water, the negative relationship should be enhanced by this factor. Taken together, the primary factors (rainfall, carbonate accumulation depth, and soil gas transport) affecting both δ¹⁸O_c and S(z) should be captured by the inverse δ¹⁸O_c-S(z) relationship (Supplementary Fig. S5). δ¹⁸O_c is thus expected to serve as a reasonable empirical proxy for S(z).

To examine the relationship between δ¹⁸O_c and S(z), we back-calculated S(z) using the clay-sized carbonate fraction of the glacial paleosol samples spanning the last 800 ky (Eq. 3 in Materials and Methods), during which CO₂ levels are known independently from the Antarctic ice cores. To propagate uncertainties from all the inputs (i.e., S(z), δ¹³C of atmospheric CO₂, soil-respired CO₂, pedogenic carbonate, and carbonate formation temperature), we adopted a Monte Carlo random sampling approach similar to the PBUQ code²⁶, which generates S(z) distributions through 10,000 iterations. During each run, input variables were randomly chosen from their normal distributions based on the mean and uncertainty of each parameter. The medians, 14th and 84th percentiles of the resulting S(z) distributions were used to represent the best estimates and the 1σ error.

Glacial S(z) estimates over the past 800 ky range between 224–542 ppm with a mean 1σ of ±86 ppm. Glacial S(z) levels are generally lower than the corresponding interglacial S(z) levels (356–815 ppm)¹⁰, in line with the overall colder and drier climate and lower soil productivity during glacial than interglacial episodes²⁷. The S(z) range is also consistent with modern S(z) measurements (572 ± 273 ppm) on the CLP during the warm, dry periods when pedogenic carbonates likely grow³⁹. Then, an exponential correlation between δ¹⁸O_c and S(z) was identified (Supplementary Fig. S6):

$${{{{\rm{S}}}}}_{({{{\rm{z}}}})}=48.472\,(\pm \! 19.747)\times {e}^{-0.2131 \; (\pm 0.0403)\times {{{\rm{\delta }}}}^{18}{{{{\rm{O}}}}}_{{{{\rm{c}}}}}}({R}^{2}=0.44,p < 0.001)$$

(1)

We next applied a bootstrap resampling technique to our samples spanning the last 800 ky, which confirmed the robustness of the empirical equation in predicting glacial S(z) (Materials and Methods).

Notably, the Zhaojiachuan data do not significantly overlap with the Fuxian data (Supplementary Fig. S6). Such a difference is anticipated as modern observations suggest lower rainfall and higher aridity in Zhaojiachuan than Fuxian, from which we would expect lower S(z) and higher δ¹⁸O_c⁴⁰. However, considering both δ¹⁸O_c and S(z) are primarily controlled by rainfall amount across the CLP^10,40, and given the close proximity (<150 km) of the two sections (Supplementary Fig. S2), it is unlikely that their δ¹⁸O_c—S(z) relationships differ significantly. We also calculated S(z) using δ¹⁸O_c—S(z) empirical equations derived from individual sections, and the resulting CO₂ estimates are within the 1σ error of those obtained from the uniform equation (Supplementary Fig. S7).

In addition, processes affecting the δ¹⁸O_c (e.g., moisture source, soil water evaporation)⁴⁰ and S(z) (e.g., soil respiration, gas diffusion controlled by soil texture)³⁴ might vary across the Pleistocene glacial cycles, leading to potential changes in the empirical δ¹⁸O_c—S(z) relation. However, temperature and precipitation reconstructions from the CLP show that variations during the early Pleistocene glacial cycles are well encapsulated in those of the last 800 ky^41,42. Moreover, the parent material of the loess-paleosol sequence remained relatively invariant over time²⁷, and C₃ plants persistently dominated the CLP (as suggested by the δ¹³C of soil organic matter, Zhaojiachuan: −24.9‰ ± 0.9‰, Fuxian: −23.6‰ ± 0.7‰). These facts mean that the edaphic and biological factors affecting S(z) likely changed little among glacial periods throughout the Pleistocene. In this case, we expect the environmental controls on δ¹⁸O_c and S(z) to remain relatively stable. Further, the δ¹⁸O_c during the past 800 ky (−11.0‰ ~ −8.7‰) that are used to generate the empirical δ¹⁸O_c—S(z) equation generally overlap with those during the early Pleistocene (−11.2‰ ~ −8.1‰). It is thus reasonable to apply the empirical model to early Pleistocene glacial samples, assuming static relationships among environmental factors (e.g., temperature, rainfall, soil texture), soil respiration, and rainfall-δ¹⁸O through time.

Applying the δ¹⁸O_c-S(z) empirical scaling relation (Eq. 1) to early Pleistocene samples yields glacial S(z) ranging between 241–551 ppm, with a mean 1σ error of ±203 ppm. S(z) estimates from both sections slightly increase from 317 ± 35 ppm (mean ± SD) in Zhaojiachuan and 355 ± 56 ppm in Fuxian in the 40k world to 355 ± 67 ppm and 411 ± 58 ppm in the 100k world, respectively (Supplementary Fig. S8). The long-term increase in S(z) indicates enhanced soil respiration, which is consistent with paleoenvironmental reconstructions from the CLP that suggest increased land surface temperature⁴² and near-constant precipitation⁴¹ during the glacials across the early Pleistocene.

The long-term glacial CO₂ decline

We compute early Pleistocene glacial CO₂ levels based on carbonate samples in the clay-sized fractions (n = 141). CO₂ uncertainties are quantified by propagating uncertainties sourced from the input variables (i.e., δ¹³C, temperature, and S(z)) using the PBUQ code based on Monte Carlo random sampling²⁶ (Materials and Methods). Best CO₂ estimates indicate a long-term decline of ~30–40 ppm, from an average of 256 ppm (SD = ± 45 ppm, n = 103) in the 40k world to 221 ppm (SD = ± 40 ppm, n = 38) during 1250–800 ka (Fig. 1c). For comparison, δ¹¹B-based glacial CO₂, which are overall higher, decreased from 272 ± 62 ppm (n = 81) to 251 ± 31 ppm (n = 79) (Supplementary Fig. S1). The decline in minimum CO₂ (on an orbital timescale) is consistent with direct measurements from the Antarctic ice cores¹² (Fig. 1b).

Notably, samples from Zhaojiachuan show slightly higher atmospheric CO₂ estimates than those from Fuxian (Fig. 1c), possibly biased by merging samples from two sections together to build a statistically significant δ¹⁸O_c-S(z) empirical equation. Nonetheless, the CO₂ variation trends in the Fuxian and Zhaojiachuan samples are identical throughout the early Pleistocene (Fig. 1c), and the differences between the two sections (~40 ppm) are much smaller compared to errors associated with individual estimates (average 1σ = ± 140 ppm). It should be noted that the paleosol-based glacial and interglacial CO₂ estimates are indistinguishable from each other¹⁰ (Supplementary Fig. S9). This is likely due to a combination of high uncertainties and incomplete documentation. Specifically, given that the CO₂ uncertainty is higher than the full amplitude of CO₂ variations (~120 ppm in the 100k world, probably less pronounced in the 40k world), our paleosols cannot resolve the glacial-interglacial CO₂ difference. Moreover, because of the dissolution and reprecipitation of pedogenic carbonates, it is unlikely that our paleosol samples recorded the full glacial-interglacial CO₂ cycle¹⁰.

Coupled glacial CO₂ drawdown and global cooling

The paleosol-derived glacial CO₂ record allows us to assess the long-term dynamics between atmospheric CO₂ and global climate. We selected three types of marine-proxy-based records that capture the large-scale variability of Earth’s climate system with sufficient resolution to resolve orbital cycles: the benthic δ¹⁸O stack¹⁹, bottom water temperature (BWT) based on benthic foraminifera Mg/Ca from DSDP Site 607 in the North Atlantic⁴³, and sea surface temperature (SST) reconstructions based on alkenone thermometry (${{{{\rm{U}}}}}_{37}^{{{{\rm{k}}}}\hbox{'}}$). The benthic δ¹⁸O represents a composite signal of global ice volume and deep ocean water temperature, which is spatially more uniform compared to global SST²². Combined with independent BWT reconstructions, these proxies provide insights into the co-evolution of ice volume and ocean temperature. It is important to acknowledge that the Mg/Ca-BWT proxy is complicated by diminished sensitivity at low temperatures and the potential for nonthermal influences⁴⁴. Nonetheless, given the current lack of a direct, high-fidelity recorder of bottom water temperature⁴⁵, we proceed with Mg/Ca-BWT record while recognizing its limitations. For SST, we first focus on the ODP Site 1143 in the Western Pacific Warm Pool (WPWP)⁴⁶, which exhibits a relatively simple response to radiative forcing. As the warmest surface ocean water on Earth, the WPWP temperature affects both the meridional and zonal thermal gradients, exerting significant influences on regional and global climate patterns, thereby representing a critical component of the global climate system⁴⁷. Unlike their Pliocene counterparts, Pleistocene ${{{{\rm{U}}}}}_{37}^{{{{\rm{k}}}}\hbox{'}}$ data from Site 1143 exhibit higher, orbitally resolved resolution, and the proxy is not saturated (when SST is at ~28 °C, ${{{{\rm{U}}}}}_{37}^{{{{\rm{k}}}}\hbox{'}}$ approaches 1). For comparison, we also included the latest global mean surface temperature (GMST) record based on a compilation of published SST records and climate model simulations⁴⁸.

Each record was divided into two subgroups (glacial vs interglacial), and the data from each subgroup were binned to a 300-ky time window to allow for direct data comparisons at the same resolution. The 300-ky time window was chosen to ensure enough data coverage (at least 20 glacial/interglacial CO₂ estimates within each time interval) such that the mean is representative, but also to allow comparison of long-term variations among individual records. Splitting the data into larger time windows does not change the following conclusions regarding the long-term trends and climate sensitivity (Supplementary Fig. 10).

Atmospheric CO₂ levels over the last 800 ky were obtained from ice-core data. Beyond 800 ka, we compiled direct CO₂ measurements from blue ice¹² as well as proxy-based CO₂ records based on paleosols¹⁰ and the boron isotope of marine carbonates^{9,14,15,16,17,49}. The alkenone-based CO₂ estimates were considered questionable due to the lack of constraints on the associated parameters and thus not included here^50,51. A recent work used leaf-wax δ¹³C from ocean sediments to reconstruct CO₂ spanning the last 1.5 Ma⁵². However, given the complex responses of leaf-wax δ¹³C to multiple environmental parameters other than atmospheric CO₂ levels (e.g., the relative contribution of C₃ and C₄ plants, temperature, water availability)^53,54,55, which were not sufficiently addressed in the original paper, we decided not to include this record. Given the age uncertainty of the blue-ice CO₂ data, the upper and lower halves of the measurements were used to represent interglacial and glacial CO₂, respectively. The Mg/Ca-based BWT record was recalculated to account for changes in seawater Mg/Ca⁵⁶ (Materials and Methods). The alkenone-based SST record was calculated using the BAYSPLINE model that better accounts for the non-linearity of the ${{{{\rm{U}}}}}_{37}^{{{{\rm{k}}}}'}$—SST relationship⁵⁷ (Materials and Methods).

Several key features emerge when comparing interglacial and glacial CO₂ separately with global climate records. First, despite an overall cooling trend, key climate conditions during interglacial maxima varied little across the Pleistocene (Fig. 2f–j), especially for benthic δ¹⁸O and WPWP-SST records. Likewise, interglacial CO₂ show no apparent long-term trend, with median CO₂ fluctuating between 220 and 282 ppm except for the Plio-Pleistocene transition (2.6–2.4 Ma) (Fig. 2j). On the other hand, glacial period benthic δ¹⁸O, WPWP-SST, and GMST records show long-term, stepwise cooling trends across the early Pleistocene (Fig. 2a–c), which align with the secular decrease of glacial CO₂ (Fig. 2d). This exercise underscores the tight coupling between atmospheric CO₂ and global climate, as well as the role of a gradually decreasing glacial CO₂ in driving the Pleistocene global cooling and the MPT.

Fig. 2: Glacial and interglacial evolution of atmospheric CO₂ and global climate.

All the records were separated into glacial (a–e on the left) and interglacial (f–j on the right) subsets and binned to a 0.3-million-year (300-ky) time window. CO₂ data beyond 800 ka were compiled paleosol- and boron-based estimates^{9,10,14,15,16,17,49} and blue-ice measurements^12,78. The medians are highlighted by horizontal lines. Gray dashed lines connect the maximum and minimum values of each time window. The long-term decline in glacial CO₂, along with the relatively stable interglacial CO₂ maxima, is broadly consistent with global temperature trends.

Climate sensitivities among glacials and interglacials

The composite CO₂ record allows us to evaluate the sensitivities of the global climate in response to CO₂ forcing among the cold glacials and warm interglacials separately. The SST-based GMST record was used here for climate sensitivity analyses (Fig. 2d, i, Supplementary Fig. S11). In paleoclimate studies, the long-term global temperature response to changes in CO₂ forcing is referred to as Earth system sensitivity (ESS)⁵⁸, which is also equivalent to the specific climate sensitivity term S_CO2. ESS accounts for both fast and slow feedbacks (e.g., ice sheets, vegetation, non-CO₂ greenhouse gases) and is different from ECS, which only includes fast-feedback processes. For close-to-equilibrium changes in the geologic past, because the annual mean global insolation changes are negligible, radiative perturbations from slow and fast feedbacks must be almost balanced (ΔF_slow + ΔF_fast ≈ 0). ECS can therefore be estimated from paleoclimate data by quantifying radiative forcings from all slow-feedback processes and removing their influences from the calculated climate sensitivity (Materials and Methods)⁵⁹. The most important slow-feedback forcing during glacial cycles is ice-sheet albedo (ΔF_LI), which is commonly used in paleoclimate studies to approximate ECS².

In this study, we first calculated ESS based on the linear regression slope (S_CO2) in the ΔGMST–ΔF_CO2 space (Fig. 3a, Materials and Methods, Eqs. 6–7). The linear regression of interglacial records yields higher p values than those of the glacial records, due to the relatively higher CO₂ uncertainty and smaller variabilities of both CO₂ and GMST estimates (Fig. 3a–c). The median value of interglacial S_CO2 is 1.7 K W⁻² m⁻¹, slightly lower than the glacial value of 2.0 K W⁻² m⁻¹ (Fig. 3a). The higher glacial S_CO2 is consistent with previous work, indicating a larger land-ice-albedo feedback affecting changes in climate among glacial than among interglacial periods^9,16. These S_CO2 values are also in line with those (~1–2 K W⁻² m⁻¹) during the Pliocene-Pleistocene transition calculated from ice-core and boron-derived CO₂ data¹⁶. Multiplied by a radiative forcing of ~3.7 W m⁻² resulting from CO₂ doubling, our S_CO2 results in ESS estimates of 6.2-7.4 K (3.2–12.0 K, 95% confidence).

Fig. 3: Glacial and interglacial climate sensitivities.

a–c ΔGMST⁴⁸ plotted against changes in different radiative forcings, including CO₂ forcing alone (ΔF_CO2), combined CO₂ and ice-sheet forcings before (ΔF_CO2,LI) and after (ΔF_CO2,LI-cal) applying the efficacy factor ε. The linear regression slopes represent climate sensitivities. Glacial (blue) and interglacial (orange) records were analyzed separately. The data points and error bars represent the means and standard deviations of all the data within each 300-ky time window. Dashed lines and shades denote linear regression lines and 95% confidence intervals. d–f Probability density distributions of climate sensitivities based on Monte Carlo random sampling (Materials and Methods). d, e correspond to (a, b), whereas f shows S_total accounting for all slow feedbacks, which approximates ECS. Solid and dashed lines denote the medians and 95% confidence intervals. Cohen’s d and p values are used to evaluate the difference between glacial and interglacial sensitivities, with d > 0.3 and p < 0.001 indicating a significant difference.

To allow comparison with published values, we next calculated specific climate sensitivity using the combined ΔF_CO2 and ΔF_LI (Materials and Methods, Eq. 8), the latter of which were from published literature based on the deconvolution of benthic δ¹⁸O stack with three-dimensional ice-sheet models, in combination with the latitudinal changes in incoming insolation⁸ (Supplementary Fig. S11). An efficacy factor ε (0.45^+0.34/_−0.2, mean ± 1σ) was then applied on ΔF_LI to account for the smaller contribution of land-ice changes to global temperature change per unit radiative forcing (K W⁻² m⁻¹) compared to atmospheric CO₂⁶⁰. The corresponding specific climate sensitivity, S_CO2,LI-cal, was calculated as ΔT/(ΔF_CO2 + ε ΔF_LI). Finally, to approximate ECS, the calculated S_CO2,LI-cal (Fig. 3c) was multiplied by a conversion factor φ (0.64 ± 0.07, mean±1σ) to account for other slow feedbacks such as vegetation and non-CO₂ greenhouse gases (S_total)³.

Accounting for slow-feedback processes improves the linear correlation between ΔGMST and ΔF (Fig. 3b, c). In particular, median values of S_CO2,LI are 0.9 and 1.3 K W⁻² m⁻¹ for interglacial and glacial periods, respectively (Fig. 3e). It should be noted that the glacial S_CO2,LI remains higher than the interglacial one after considering the ice-sheet albedo feedback, indicating that the radiative response to non-ice-sheet feedbacks, including both fast (e.g., aerosol, sea ice) and/or slow feedbacks (e.g., vegetation) were probably stronger among interglacial periods compared to glacials. The S_CO2,LI translate to interglacial and glacial ESS estimates of 3.3 K (1.8–5.5 K, 95% confidence) and 4.8 K (3.0–7.6 K, 95% confidence), respectively, which are consistent with previously reported ESS based on S_CO2,LI from the Pliocene-Pleistocene glacial cycles (3.5-5.7 K)^8,16,61.

The difference between glacial and interglacial ΔGMST - ΔF_total regression slopes (S_total) is negligible after considering all slow-feedback processes, with median S_total values of 0.9 and 1.0 K W⁻² m⁻¹ for glacial and interglacial periods, respectively (Fig. 3f). The corresponding ECS estimates are 3.3 K (2.1–6.3 K, 95% confidence) and 3.7 K (1.7–6.3 K, 95% confidence), which aligns well with the commonly accepted ECS range of 2.6–4 K based on instrumental records and process understanding⁶². Notably, evidence from both model and data indicates state-dependency of ECS, which refers to changes in the efficacy of feedback processes under different background climate conditions (e.g., temperature, plate configuration, ice sheets), leading to a non-linear relationship between global temperature and CO₂ forcing⁶³. For instance, ECS estimates based on observations from glacial-interglacial cycles found lower sensitivity to forcing (smaller ECS) during colder periods compared to warmer periods^61,64. However, ECS estimates based on our compiled CO₂ records, after accounting for different efficacies of ice-sheet and CO₂ forcing as well as other slow-feedback processes, remained consistent among glacial and interglacial periods, indicating no apparent state-dependency. The lack of state-dependency suggests that fast feedbacks maintained relatively constant behavior despite the contrasting climate states of cold glacial and warm interglacial periods.

Methods

Sampling and chronology

We collected paleosol samples from two loess-paleosol sequences located in the central CLP (Fig. S2). For the Zhaojiachuan section (N 35°46′38″ E 107°47′25″), soil samples were collected from the outcrops along the hillside at 10 cm intervals. We trenched the soil profiles 2 m deep before sampling to avoid regolith contamination. For the Fuxian section, we drilled a 206-m core from the highest terrace near Fuxian County (N 36°9′33″ E 109°27′6″), with the upper 161.7 m being the Quaternary loess-paleosol sequence. Soil deposition ages of the two sections are established by MS chronostratigraphy with respect to the Lingtai section, the chronology of which was determined by paleomagnetic polarity and astronomical tuning⁶⁵.

The ages of pedogenic carbonates in this study were determined by the deposition ages of paleosol layers within which they are embedded. Notably, this age assignment represents their maximum ages as pedogenic carbonate grows below the soil surface. Comparison between loess deposition ages and the radiocarbon ages of clay-sized carbonates formed during the last glacial period suggests that the carbonates were formed at 0-50 cm depth, which corresponds to a maximum age difference of 10-ky (Fig. S4). Such an age offset is substantially smaller than the time span of each glacial period (100 ky). To avoid pedogenic carbonates formed during interglacial periods that were translocated into the underlying glacial units, samples were selected from the bottom part of each glacial unit.

Particle size separation

To avoid contamination of detrital carbonates, we target calcites within the clay-sized fractions (<2 μm) of bulk paleosols. This approach has been successfully applied to extract pedogenic carbonates from paleosols in previous studies⁴⁰. Due to the preferential dissolution and precipitation of fine-grained carbonate by soil solution, pedogenic carbonate dominates the clay-sized fractions of loess-parented soils⁴⁰. The clay-sized particles were extracted through centrifugal sedimentation following Stocks’ law. Specifically, a sample split of ~10 g was ultrasonically dispersed in deionized water and then centrifuged at 2000 rpm for 3 minutes. The upper turbid solution was transferred and centrifuged again at 5000 rpm for 15 minutes, with the bottom precipitation being the clay-sized fraction. We repeated the above steps multiple times until little suspension existed in the solution. The precipitates were oven-dried at 60 °C and then ground into powder with an agate mortar and pestle for subsequent analyses. The micromorphology and geochemistry of our samples corroborate a minor contribution from detrital carbonates. Specifically, scanning electron microscopy imaging reveals that the clay-sized fractions are dominated by nanoscale NFC (Supplementary Fig. S3). Moreover, the radiocarbon ages of clay-sized carbonates are close to those of coeval soil organic matter, and the depositional ages of loess from the corresponding layer (Supplementary Fig. S4), indicating a minor contribution of the radiocarbon-dead, detrital carbonates.

Stable isotope analyses

We selected 181 paleosol samples from the two loess sections on the CLP (96 from Fuxian and 85 from Zhaojiachuan) for CO₂ reconstruction. For δ¹³C and δ¹⁸O analyses, sample splits of 50 mg were first treated with 10% H₂O₂ to remove soil organic matter. The residues were then oven-dried and ground into powder for homogenization. The samples were measured on a Thermo-Finnigan MAT 253 IRMS attached with a Kiel IV carbonate device (75 °C reactions in 100% H₃PO₄). The isotopic values are reported in the δ notation (normalized to the VPDB standard) with permil (‰) unit. Replicates of samples (n = 5) were analyzed, yielding a standard deviation of 0.03‰ for both δ¹³C and δ¹⁸O. For δ¹³C_o analyses, sample splits of 200 mg were reacted with 1 N HCl overnight to remove carbonates. HCl was added multiple times until no bubbles were produced to ensure the complete removal of inorganic carbon. The samples were subsequently rinsed with deionized water repeatedly until pH reached neutral, oven-dried, and ground into powder. 25–30 mg of sample was sealed in a tin capsule and analyzed using a Costech 4010 Elemental Analyzer coupled to a Thermo Delta V IRMS system. δ¹³C_o values were corrected to the VPDB scale with an average standard deviation of 0.2‰ from replicate analyses of samples (n = 3).

Radiocarbon analyses

To examine the potential contamination of detrital carbonate and the illuviation of pedogenic carbonate, we performed radiocarbon analysis on both the carbonate (n = 9) and soil organic matter (n = 4) in our clay-sized samples from the loess-paleosol unit corresponding to the Holocene and last glacial period (Supplementary Fig. S4). The measurement was carried out at the Keck-Carbon Cycle AMS facility at the University of California, Irvine. There, sample splits were combusted to CO₂, cryogenically purified, graphitized, and measured on an NEC Compact (1.5 SDH) Accelerator Mass Spectrometer. Radiocarbon activities are reported in Δ¹⁴C (‰), which was calculated from fraction modern carbon (F_m) and corrected for the decay of the radiocarbon standard since 1950⁶⁶. Radiocarbon ages were converted to calendar ages using the INTCAL20 calibration curve⁶⁷.

The paleosol-CO₂ method

The paleosol-CO₂ proxy is based on the steady-state diffusion reaction model²⁵. Specifically, the δ¹³C of CO₂ in soil pore space (δ¹³C_s) is controlled by two endmembers—CO₂ sourced from the respiration of plant roots and soil microbes, and atmospheric CO₂ penetrating the soil–air interface through diffusion²⁴. The equation is as follows:

$${{{\rm{\delta }}}}^{13}{{{{\rm{C}}}}}_{{{{\rm{s}}}}}=\frac{{{{\rm{\delta }}}}^{13}{{{{\rm{C}}}}}_{{{{\rm{a}}}}}\times {[{{{{\rm{CO}}}}}_{2}]}_{{{{\rm{atm}}}}}+{{{\rm{\delta }}}}^{13}{{{{\rm{C}}}}}_{{{{\rm{r}}}}}\ast \times {{{{\rm{S}}}}}_{({{{\rm{z}}}})}}{{[{{{{\rm{CO}}}}}_{2}]}_{{{{\rm{atm}}}}}+{{{{\rm{S}}}}}_{({{{\rm{z}}}})}}=\frac{{{{\rm{\delta }}}}^{13}{{{{\rm{C}}}}}_{{{{\rm{a}}}}}\times {[{{{{\rm{CO}}}}}_{2}]}_{{{{\rm{atm}}}}}+{{{\rm{\delta }}}}^{13}{{{{\rm{C}}}}}_{{{{\rm{r}}}}}\ast \times {{{{\rm{S}}}}}_{({{{\rm{z}}}})}}{{[{{{{\rm{CO}}}}}_{2}]}_{{{{\rm{soil}}}}}}$$

(2)

where δ¹³C_a and δ¹³C_r^∗ represent the δ¹³C of atmospheric CO₂ and soil-derived CO₂ (including both autotrophic and heterotrophic respiration), respectively; [CO₂]_atm and [CO₂]_soil are atmospheric CO₂ and total-soil CO₂ concentrations, respectively; S(z) is the concentration of soil-respired CO₂ at the depth z of pedogenic carbonate growth. At steady-state diffusion, the δ¹³C of CO₂ in the soil pore space sourced from the respiration (δ¹³C_r^∗) can be calculated from the δ¹³C of respired CO₂ (δ¹³C_r) via diffusion coefficients²⁵, and we get the paleosol-CO₂ equation by rearranging Eq. 2:

$${[{{{{\rm{CO}}}}}_{2}]}_{{{{\rm{atm}}}}}={{{{\rm{S}}}}}_{({{{\rm{z}}}})}\times \frac{{{{\rm{\delta }}}}^{13}{{{{\rm{C}}}}}_{{{{\rm{s}}}}}-1.0044{{{\rm{\delta }}}}^{13}{{{{\rm{C}}}}}_{{{{\rm{r}}}}}-4.4}{{{{\rm{\delta }}}}^{13}{{{{\rm{C}}}}}_{{{{\rm{a}}}}}-{{{\rm{\delta }}}}^{13}{{{{\rm{C}}}}}_{{{{\rm{s}}}}}}={{{{\rm{S}}}}}_{({{{\rm{z}}}})}\times {{{\rm{R}}}}$$

(3)

where 1.0044 and 4.4 are diffusion coefficients resulting from the different diffusivity of ¹²CO₂ and ¹³CO₂ in soil pores. The R values, which can be solved by the three δ¹³C parameters, represent the ratio of atmospheric CO₂ and soil-respired CO₂ in the soil pore space during pedogenic carbonate growth. Under surficial climatic conditions, pedogenic carbonates formed in isotopic equilibrium with soil CO₂, and the fractionation between calcite and CO₂ is temperature-sensitive⁶⁸. δ¹³C_s can thus be solved by the δ¹³C of pedogenic carbonate (δ¹³C_c) with calcite crystallization temperature (T).

Defining input parameters

The δ¹³C_a is estimated by the δ¹³C of marine carbonates, which records the δ¹³C of ocean dissolved inorganic carbon that is sensitive to changes in δ¹³C_a⁶⁹. We do not have direct T measurements in this study. Nonetheless, the paleosol-CO₂ method is not sensitive to T compared to other inputs (e.g., S(z), δ¹³C_r), with 5 °C uncertainty contributing to less than 10% of the total uncertainty of the resulting CO₂ estimate⁷⁰. Soil surface temperatures reconstructed from biomarkers on the CLP reveal a small, gradual warming trend of ~1.1 °C across the Pleistocene accompanied by large fluctuations⁴². Notably, due to increased vegetation coverage during interglacial periods, there are no apparent soil temperature differences between glacial and interglacial periods. In this case, considering the dampening of soil temperature with depth, we assigned a uniform T using modern mean annual soil temperatures at 20 cm depth from each sampling site (http://www.data.cma.cn). The 1σ error was set to ±3 °C based on the variations of reconstructed soil surface temperatures on the CLP over the Pleistocene glacial cycles^42,71. Importantly, as both the late Pleistocene S(z) estimates used to calibrate the δ¹⁸O-S(z) relationship and the early Pleistocene CO₂ estimates were calculated using the same temperature, if the actual Ts are systematically different from our assumed values, their influences are inherently canceled in our approach. The δ¹³C_r is approximated by measuring the δ¹³C of soil organic matter (δ¹³C_o) from the same sediment layer where pedogenic carbonates were collected. Notably, studies on modern soil and paleosol profiles indicate ¹³C/¹²C fractionation accompanying organic matter decomposition^72,73. We applied a −1 ± 0.5‰ (mean±1σ) correction on δ¹³C_o data to account for the decomposition-related fractionation based on the difference between δ¹³C of soil organic matter occluded in calcite nodules and those in bulk paleosols, the former of which are considered resistant to decomposition⁷³. The δ¹⁸O_c - S(z) relation (Eq. 1) was used to estimate S(z), with the 1σ error propagated through Monte Carlo random sampling.

A MATLAB-PBUQ code based on Monte Carlo simulations²⁶ was used to calculate CO₂ and propagate errors associated with input variables. The medians, 16th and 84th, and 2.5th and 97.5th of the resulting CO₂ distributions were reported as the best estimates with 1σ and 2σ errors. The time series of both the raw input parameters (δ¹³C_c, δ¹⁸O_c, δ¹³C_o, δ¹³C_a) and intermediate parameters (S(z), δ¹³C_s) used for calculating CO₂ were provided in Supplementary Figs. S12 and S8, respectively.

Bootstrap sampling

We divided the 800-ky samples (n = 40) into two groups—one training group used to generate the δ¹⁸O_c—S(z) empirical scaling relation and one test group that calculated CO₂ with S(z) estimated from the δ¹⁸O_c—S(z) relation established using the training group data. For a given training group size n, we randomly drew n samples from the population, calculated CO₂ for the remaining (40–n) samples, and examined the mean relative difference (χ) between estimated CO₂ and the corresponding ice-core CO₂:

$$\chi \,=\,\frac{1}{40-n}\,{\sum }_{i=1}^{40-n}\left(1-\frac{{[{{\mathrm{calculated}}}\,{{{\mathrm{CO}}}}_{2}]}_{i}}{{[{{\mathrm{ice}}}\,{{\mathrm{core}}}\,{{{\mathrm{CO}}}}_{2}]}_{i}}\right)$$

(4)

The bootstrap sampling was repeated 10,000 times to obtain the corresponding χ values. The χ distributions cluster around −0.05 regardless of the training group size (n = [10,30]), with 95% of the data points falling within ~−20/ + 10% difference (Supplementary Fig. S13). It is noteworthy that there is a negative skew for the χ distributions. However, such deviations are minor, as the mean χ of −0.05 translates to 9–11 ppm when CO₂ levels are 174 to 218 ppm (highest and lowest ice-core CO₂ values used for comparison). Therefore, this test demonstrates the robustness of the δ¹⁸O_c—S(z) scaling approach, lending support for applying this approach to resolve S(z).

Recalculating BWT and SST records

The original BWT record from North Atlantic⁴³ assumed a constant seawater Mg/Ca throughout the Pleistocene. Although both Mg and Ca have long residence time in the ocean, recent studies suggest a non-negligible long-term increase in seawater Mg/Ca over the past 30 million years due to changes in hydrothermal activity, weathering, and carbonate deposition^56,74. We used the following equation to recalculate BWT accounting for changes in seawater Mg/Ca based on the calibration equation⁵⁶ and the original equation⁴³:

$${{{\rm{BWT}}}}=\left(\frac{{\left[\frac{{{{\rm{Mg}}}}}{{{{\rm{Ca}}}}}\right]}_{{{{\rm{sw}}}},0}}{{\left[\frac{{{{\rm{Mg}}}}}{{{{\rm{Ca}}}}}\right]}_{{{{\rm{sw}}}},{{{\rm{t}}}}}}\times {\left[\frac{{{{\rm{Mg}}}}}{{{{\rm{Ca}}}}}\right]}_{{{{\rm{foram}}}}}-1.16\right)/0.15$$

(5)

Where [Mg/Ca]_sw,0, [Mg/Ca]_sw,t, [Mg/Ca]_foram are the Mg/Ca ratios of modern seawater, seawater of the time of interest, and foraminifera, respectively. [Mg/Ca]_sw,0 is set to 5.2 mmol/mol⁷⁵. [Mg/Ca]_sw,t is based on a fourth-order polynomial curve fit through compiled [Mg/Ca]_sw proxy records⁵⁶.

A global compilation of core-top samples shows strong seasonal production of alkenones and significant attenuation of the ${{{{\rm{U}}}}}_{37}^{{{{\rm{k}}}}\hbox{'}}$ response to higher temperature as it reaches saturation⁵⁷. To account for these observations, we recalculated the ${{{{\rm{U}}}}}_{37}^{{{{\rm{k}}}}\hbox{'}}$-based SSTs by applying the original ${{{{\rm{U}}}}}_{37}^{{{{\rm{k}}}}\hbox{'}}$ data to a Bayesian B-spline regression model, BAYSPLINE⁵⁷.

Climate sensitivity analyses

The ESS, or S_CO2, is defined as the long-term temperature response (ΔT) to a given change in CO₂ forcing (ΔF_CO2)⁵⁸:

$${S}_{{{{\rm{CO}}}}2}=\frac{\Delta {{{\rm{T}}}}}{\Delta {{{{\rm{F}}}}}_{{{{\rm{CO}}}}2}}$$

(6)

where both ΔT and ΔF_CO2 refer to changes relative to the pre-industrial condition. Here we applied the latest global mean surface temperature record (ΔGMST), which is based on a compilation of SST records⁴⁸. The ΔF_CO2 can be related to changes in atmospheric CO₂ levels by accounting for the logarithmic dependence of the infrared radiation absorption on CO₂:

$$\Delta {{{{\rm{F}}}}}_{{{{\rm{CO}}}}2}=5.35\times \,{{\mathrm{ln}}}({{{{\rm{CO}}}}}_{2}/{{{{\rm{C}}}}}_{{{{\rm{o}}}}})$$

(7)

where C_o is the pre-industrial level of 278 ppm. To account for radiative forcings resulting from all slow-feedback processes and estimate ECS, we used the following equation derived from Stap et al.⁶⁰:

$${{{\rm{ECS}}}}=\varphi \frac{\Delta {{{\rm{GMST}}}}}{\Delta {{{{\rm{F}}}}}_{2\times {{{\rm{CO}}}}2}+\Delta {{{{\rm{F}}}}}_{{{{\rm{LI}}}}}\times \varepsilon }$$

(8)

where ΔF_LI is the ice-sheet forcing obtained from Köhler et al.⁸, ε is the efficacy factor (0.45^+0.34/_−0.2, mean±1σ) that accounts for the smaller radiative efficacy of ice-sheet feedback compared to atmospheric CO₂⁶⁰, and φ is a conversion factor (0.64 ± 0.07, mean ± 1σ) that represents radiative forcings from other slow feedbacks³. ΔF_2xCO2 is the radiative forcing resulting from a doubling CO₂ (~3.7 W/m²)⁷⁶. To generate the probability density distributions of the calculated climate sensitivities, a value was randomly sampled from normal distributions defined by the mean value and standard deviation of each input parameter (ΔGMST, CO₂, ΔF_LI, φ, ε) for each 300-ky time window, forming the basis for generating a linear regression slope between ΔGMST and ΔF. We performed 100,000 iterations and retained the slopes with p values below 0.01. The linear regression slopes between ΔGMST and ΔF (change relative to the pre-industrial conditions) indicate climate sensitivities, with steeper slopes indicating higher sensitivity.