Asynchrony between Antarctic temperature and CO2 associated with obliquity over the past 720,000 years

The δD temperature proxy in Antarctic ice cores varies in parallel with CO2 through glacial cycles. However, these variables display a puzzling asynchrony. Well-dated records of Southern Ocean temperature will provide crucial information because the Southern Ocean is likely key in regulating CO2 variations. Here, we perform multiple isotopic analyses on an Antarctic ice core and estimate temperature variations at this site and in the oceanic moisture source over the past 720,000 years, which extend the longest records by 300,000 years. Antarctic temperature is affected by large variations in local insolation that are induced by obliquity. At the obliquity periodicity, the Antarctic and ocean temperatures lag annual mean insolation. Further, the magnitude of the phase lag is minimal during low eccentricity periods, suggesting that secular changes in the global carbon cycle and the ocean circulation modulate the phase relationship among temperatures, CO2 and insolation in the obliquity frequency band.

P recise knowledge of the relationship between changes in temperature, atmospheric CO 2 and solar insolation is essential to understanding Earth's climate system. The values of a temperature proxy, the hydrogen isotopic composition (δD), in the Antarctic EDC ice core 1,2 have varied in parallel with CO 2 concentrations over the past 800 thousand years (kyr; r 2 = 0.82) 3 . However, δD apparently leads CO 2 variations. For example, during the last termination (TI), the start of Antarctic warming has been estimated to be synchronous with CO 2 increase 4 or to lead CO 2 increases by 800 ± 600 years 5 on the East Antarctic Plateau. The lead is ca. 2000 years at a West Antarctic site 6 . Over the past 420 kyr, the Vostok ice core shows that the Antarctic δD temperatures lead the CO 2 variations by 1.3 ± 1.0 kyr 7 . During the lukewarm interglacials (430-650 kyr BP), Antarctic δD leads CO 2 by 1900 years, and the correlation between CO 2 and δD is weaker (r 2 = 0.57), as determined from the EDC core 8 .
Although the mechanisms underlying the coupling and the phase lags remain unclear, the Southern Ocean region, rather than Antarctica, is thought to play the central role in regulating CO 2 variations 9,10 . A box model, for example, estimated a ca. 60% increase in CO 2 during TI that is attributable to direct and indirect temperature effects, such as changes in sea ice cover and vertical mixing in the Southern Ocean 9 . On millennial time scales, a multi-proxy study suggests that an antiphased hemispheric temperature response to ocean circulation changes resulted in Antarctic temperatures leading global temperatures and CO 2 during TI 11 . On orbital time scales, the latitudinal temperature differences between Antarctica and the surrounding ocean may arise from annual mean insolation (AMI) variations because the amplitude of AMI variations is largest in the polar regions and smallest in the mid-latitude regions [12][13][14][15][16] . The AMI is paced only by the 41-kyr periodicity of the Earth's obliquity 17 . Indeed, a strong 41-kyr cycle that is likely related to the local AMI variations was recognized in the Antarctic temperature record obtained from the Vostok ice core in the 1980s 15 . However, uncertainties in the age models of the ice cores and ocean sediments limit our understanding of the potentially different time lags between Antarctic and Southern Ocean temperatures relative to AMI changes. Therefore, well-dated surface temperature records with high temporal resolution from the Southern Ocean provide crucial information.
In addition to these climatic mechanisms, the validity of δD as a temperature proxy should be considered. While this proxy depends on Antarctic site temperatures (ΔT site ), it is also affected by the extent of fractionation-associated rainout from the water vapour as it is transported from its moisture source in the ocean to the site where the precipitation occurs. After correcting the δD variations for this moisture source effect, the ΔT site record shows a stronger correlation with CO 2 over the past 350 kyr 18 , suggesting a potential bias in the use of δD as a temperature proxy. However, the effects of moisture source corrections are unknown prior to 420 kyr BP 19 . The lack of long records prevents elucidation of the potential influence of the 400-kyr eccentricity cycle on the relationship among AMI, CO 2 and Antarctic and ocean temperatures.
To investigate the relationship between temperatures and CO 2 concentrations, we estimated ΔT site and ocean surface temperatures (ΔT source ) using new δD and deuterium excess records from the Antarctic Dome Fuji (DF) ice core, which spans the past 720 kyr. The new ΔT site and ΔT source records enable us to compare the pattern and timing of temperature variations between the Antarctic Plateau and its oceanic moisture source using the same age scale from that of the DF ice core. Our data extend the longest (420-kyr) record of ΔT site 19 by 300 kyr, and they reveal the impact of moisture source corrections during the lukewarm interglacials.
The correlation between ΔT source and CO 2 is stronger than that between δD and CO 2 . Over the entire periods covered by the extended records, changes in local solar insolation, paced by obliquity, strongly affects ΔT site . At the obliquity periodicity, the changes in ΔT site and ΔT source are delayed with respect to AMI. Further, the magnitude of the phase lag is minimal during the period of low orbital eccentricity, suggesting that the phase modulation is related to secular changes in the global carbon cycle and ocean circulations.

Results
Dome Fuji isotope and temperature records. We used the second DF ice core (DF2; 77˚19′ S, 39˚42′ E, 3810 m above sea level) 20 to obtain a 720-kyr deuterium excess (d = δD-8δ 18 O) record. The δD and δ 18 O values of the ice between the depths of 2399.5 and 3035.1 m (297-715 kyr BP) were measured at 10-cm intervals. The new DF2 data were combined with earlier data from the first Dome Fuji core (DF1 21,22 ) and were plotted on the AICC2012 time scale 23 . The relationships among δD, d, ΔT site and ΔT source were quantified using a mixed cloud isotopic model (Methods). In this study, temperatures are expressed as deviations, Δ, from the modern value (the average of the past 2 kyr). ΔT source is a proxy for temperature in moisture source regions 19,22 , and the major moisture source for modern precipitation at DF is estimated to lie in the South Atlantic and Indian Oceans between 38 and 65˚S, based on backwardtrajectory calculations [24][25][26] (Fig. 1).
The DF2 core provides detailed δD profiles over the past 720 kyr (Fig. 2). The δD record from DF covaries linearly with that from EDC 1,2 (R 2 = 0.91, with an EDC/DF slope of 1.1) over the past 720 kyr. With their higher sampling resolution (10 cm vs. 55 cm), the DF data depict the paleoclimate signals in greater detail than the EDC core. However, the deepest part appears to have been smoothed by ice diffusion, a process also observed in the 11cm samples from the EDC core that correspond to Marine Isotope Stage (MIS) 11 ( Supplementary Fig. 1 The DF ΔT site correlates well with DF δD at glacial-interglacial time scales over the entire record (Fig. 2). Millennial-scale events during glacial periods in the δD record are also identifiable in the ΔT site record ( Supplementary Fig. 2). The ΔT site values range from −8.0°C (MIS 12.2) to 4.0°C (MIS 9.3) when 2-kyr mean values are used (Fig. 2). The ΔT site record shows the lesspronounced interglacial maxima prior to~430 kyr (the Mid-Brunhes Event, MBE), as suggested by the EDC δD variations 1,2 .
The DF2 core d record is shown in terms of the logarithmic definition of d (hereafter d ln ; Fig. 2), which reflects moisture source conditions better than the traditional linear definition 22 ( Supplementary Fig. 3). Recent modelling studies also present evidence supporting the logarithmic definition 27,28 . The glacial-interglacial variations in ΔT source are generally similar to the variations in d ln (Fig. 2). The DF2 ΔT source values range from −6.0°C in MIS 12.2 to 2.2°C in MIS 9.3. During glacial inceptions, ΔT source remains warm, whereas ΔT site begins to cool (for example, during MIS 11.2; Fig. 3a). Other features also emerge during the lukewarm interglacials. Notably, a ca. 2°C drop in ΔT site during MIS 13.2 has no counterpart in ΔT source (Fig. 3a).
To estimate temperatures, we used the same parameters used in a previous study 22 (Methods). The use of these values produces glacial-interglacial variations in ΔT source that are larger than those presented by previous studies 19,29 , resulting in good agreement between the DF ΔT source record and a stacked SST record 30 over the past 150 kyr 22 . Here, to evaluate the reliability of our ΔT source estimates over multiple glacial cycles, we constructed a stacked sea surface temperature (SST) record based on 17 individual deep-sea sediment cores obtained in the source region (Methods and Supplementary Fig. 4). The stacked SST record shows remarkable similarities with our ΔT source record in terms of both amplitudes and the patterns of variation over the past 440 kyr, and they agree within mutual amplitude and age uncertainties (Fig. 2d). Hence, the effects of shifts in the moisture source associated with westerly wind displacement 28 are limited in the DF record on glacial-interglacial time scales. Between the preand post-MBE periods, ΔT source exhibits an increase in amplitude of only 17%, as estimated using standard deviations 1 . This result is consistent with the overall concept that changes associated with the MBE are less prominent at low latitudes than at high latitudes 31 . We thus interpret our ΔT source reconstruction to be representative of the average changes in SSTs over broad regions of the oceanic moisture source.

Discussion
Throughout the entire record, both ΔT site and ΔT source covary with CO 2 (R 2 = 0.78 and 0.77, respectively), and these correlations are significantly stronger than that between δD and CO 2 (R 2 = 0.70, see Methods). The only exception for the strong coupling between ΔT source and CO 2 is observed during MIS 12.2, during which the ΔT source shows exceptional cooling (Fig. 3a). This observation suggests that Southern Ocean temperatures experienced exceptional cooling during MIS 12 (see discussion below).
The weakest correlation between δD and CO 2 is observed in the EDC core during the lukewarm interglacials 8 . During this period, the correlation between DF ΔT site and the composite CO 2 record 32 (R 2 = 0.76) is stronger than that between δD and CO 2 (R 2 = 0.66, Fig. 3a). We also obtained a high correlation between the records of ΔT source and CO 2 concentrations during the lukewarm interglacials (R 2 = 0.80, Fig. 3a). During MIS 13.2, for example, ΔT source and CO 2 remain at levels similar to those of MIS 13.1 and MIS 13.3, whereas ΔT site exhibits a ca. 2°C drop.
Despite the overall correlation between δD and ΔT site , the ΔT site record lags the δD record by 0.9 ± 0.1 kyr in the obliquity band ( Supplementary Fig. 5), which results in a smaller phase lag between ΔT site and CO 2 than that between δD and CO 2 (Fig. 3c). Therefore, our data suggest that the lead in Antarctic δD temperatures (i.e. temperature without correcting for source effects) over CO 2 is partly attributable to the effects of the moisture source on δD temperatures over the past 720 kyr in the obliquity band. These results suggest that the importance of moisture source effects for the obliquity signal in δD. Thus, the source effect must be considered in future research about the relationship between Antarctic temperatures and CO 2 .
The similarities and differences between temperatures and CO 2 concentrations mainly emerge from the 41-kyr obliquity periodicity. Spectral analyses reveal a smaller power in the obliquity frequency range for CO 2 and ΔT source than for ΔT site and δD (Fig. 3b). Indeed, periodic obliquity variations remain in the residuals from linear regression between δD and CO 2 , but not for ΔT source and CO 2 (Fig. 3a). Within this frequency range, the CO 2 variations display higher coherence with ΔT source than with ΔT site or δD (Fig. 3c). These results show that, within the obliquity frequency band, the CO 2 variations are not tightly coupled with temperatures on the East Antarctic Plateau (ΔT site or δD). Rather, the correlation between CO 2 and ΔT source suggests a close link  Fig. 2 Isotope records from the DF1 and DF2 ice cores. Isotope records from DF1 (grey) and DF2 (black) for a δD and b d ln , as well as records of c ΔT site (red) and d ΔT source (blue) for DF. The black line indicates the stacked SST record within the moisture source region for precipitation (grey shading represents the range of variability) ( Supplementary Fig. 4). Temperatures are shown as deviations from the modern value (i.e. the average of the past 2 kyr). The ΔT site and ΔT source records were resampled at a 2-kyr interval for clarity. Numbers indicate Marine Isotope Stages between surface temperature changes in the Southern Ocean and the global carbon cycle.
Despite the strong correlations between ΔT source and CO 2 , ΔT source lags CO 2 slightly in most frequency bands (Fig. 3c), most likely because of the large heat inertia of the Southern Ocean 33 . Furthermore, DF ΔT site leads ΔT source by 2.8 ± 0.6 kyr ( Supplementary Fig. 5) in the obliquity band. We should note that this analysis is focused on changes over orbital time scales, not millennial time scales, over which Antarctic warming is passively controlled by the Southern Ocean warming because of the thermal bipolar seesaw 33,34 . Within the obliquity frequency band, our analyses suggest that temperature variations in a Age (kyr BP)  Antarctica have led ocean temperatures throughout the past 720 kyr. This phenomenon is most likely explained by the strong influence of local AMI on ΔT site . A strong 41-kyr periodicity can be found in the temperature gradient record (ΔT grad = ΔT source -ΔT site ) (Fig. 3b). A decrease in obliquity increases the AMI gradient between the middle and high latitudes 17 , which covary in phase with the obliquity signal 17,35 . Thus, the changes in obliquity correlate closely with the AMI gradient between DF (77°S) and the moisture source region (38-66°S). The ΔT grad record is negatively correlated with the obliquity (Fig. 3a). This result is qualitatively consistent with the latitudinal temperature pattern expected from the local insolation gradient.
The impact of the differences in AMI on the amplitudes of ΔT site and ΔT source was evaluated by filtering the records in the obliquity band (Fig. 4). The range (i.e. difference between maximum and minimum) of the filtered ΔT site record was 3°C (Fig. 4b), which is close to the ca. 2.5°C changes simulated by a general circulation model 13 . The amplitude of ΔT site is twice as large as that of ΔT source when it is filtered in the obliquity range (Fig. 4c). Although the large amplitude of ΔT site expressed in the obliquity range is likely affected by AMI, the amplitude of AMI changes in the DF area is six times greater than that of the moisture source region (Fig. 4b, c). Accounting for the mean present-day planetary albedo, the effective shortwave forcing is reduced particularly strongly over Antarctica 12 . With this albedo effect, the site/source ratio for the surface net downward flux is 2.4:1 (Methods). Thus, the difference is significantly reduced, and roughly consistent with the ΔT site /ΔT source ratio. Remaining difference would be balanced by other compensation mechanisms, such as the transport of heat from the low to the high latitudes 36 , and latitudinal contrasts in the cloud feedback, which is negative near 60°S and positive at low latitudes 37 .
The phase relations between the temperature proxies and AMI reveal a unique characteristic of the temperature responses to AMI. On average, ΔT site is delayed with respect to AMI (or obliquity) by 4.1 ± 2.7 kyr at the obliquity period (Fig. 4b), as was previously shown for the EDC 2 and DF1 cores 21  also delayed relative to AMI by 7.5 ± 2.9 kyr at the obliquity period (Fig. 4c). Interestingly, the filtered ΔT grad and the AMI gradient are almost synchronous (Fig. 4f). Their lag in the obliquity band is 1.9 ± 2.6 kyr, which lies within the uncertainty of the age scale 23 . This apparent synchronization can be simply explained by the fact that the delay in ΔT site relative to AMI is cancelled out by that of ΔT source relative to AMI. Thus, the ΔT grad appears to be directly forced by the AMI gradient and obliquity without a significant phase lag. An increase in the AMI gradient enhances the degree of poleward moisture transport 35 , and results in increased snowfall and ice sheet volume in the Northern Hemisphere. Concurrently, an enhanced southward latent heat transport is expected to offset local, insolation-driven Antarctic cooling 12 . These positive and negative feedback mechanisms potentially result in the lead and lag of Antarctic temperatures relative to the AMI variations.
A closer look at the phase lag between ΔT site and AMI reveals that the magnitude of the phase lag varies with the eccentricity period of ca. 400-kyr. Large delays in ΔT site relative to AMI were observed during 100-300 kyr BP and 500-650 kyr BP (Fig. 4b).
The phase lags become small when eccentricity is small (during 350-450 kyr BP), when ΔT site and AMI are almost synchronous. To illustrate this 400-kyr phase modulation, the amplitudes of the filtered ΔT site and AMI records were normalized to a standard deviation of 1, and the difference between them is shown in Fig. 4g. Because a smaller phase lag results in a smaller difference, the amplitude of the filtered ΔT site -AMI difference record reaches a minimum during 350-450 kyr BP (Fig. 4g).
As seen in the ΔT site record, the obliquity-filtered ΔT source and CO 2 also show varying phase lags with respect to obliquity with a ca. 400-kyr eccentricity cycle (Fig. 4c, d). On average, the filtered CO 2 record shows a delay of 7.0 ± 2.9 kyr with respect to obliquity. These phase lags are significant during most of the studied period because they are larger than the uncertainty of AICC2012, which ranges from ±1.7 to ±4.8 kyr (±2.6 kyr, on average) over the past 100-720 kyr 23 . Large uncertainties were expected during MIS 11-12 because of the lack of age markers 23 . However, an abrupt decrease in δ 18 O values seen in Chinese stalagmites dated independently using the U/Th technique 38 coincides with an abrupt increase in EDC CH 4 39 at Termination V, which supports the accuracy of the AICC2012 age scale.
Interestingly, an independently dated benthic foraminiferal δ 18 O record also shows a similar varying phase with respect to obliquity 40 (Fig. 4e). When filtered in the obliquity band, the benthic δ 18 O data suggest that the 41-kyr component of the ice volume changes in the Northern Hemisphere are also delayed relative to obliquity, and the ice volume and obliquity are almost synchronous at the period of the eccentricity minimum. Thus, the delayed responses relative to obliquity are observed not only for ΔT site , but also for ΔT source , CO 2 and a proxy for ice volume. Therefore, our data do not support the hypothesis of a direct influence of local solar insolation on Antarctic temperatures 15,16 without any link to the Northern Hemisphere 16 . Rather, the millennial-scale time delay in ΔT site relative to AMI suggests the influence of 'slow' feedbacks, such as changes in greenhouse gases and/or global ice area/volume 41,42 during periods of large eccentricity.
We next attempt to determine whether ice volume or CO 2 is more directly related to the varying phase lag at the 400-kyr periodicity. Although modelling results suggest that the Eurasian ice sheet responds to insolation forcing at the 41-kyr and 23-kyr periodicities without a significant 100 kyr cycle 41 and that Antarctic ice volume varied with a periodicity of 400-kyr 43 , little evidence indicates a link between the phase lag and AMI. In an experiment with constant CO 2 , an ice sheet model could not reproduce the decrease in ice volume during MIS 11 because of the small amplitude of precession 44 . This result suggests that changes in ice volume are sensitive to atmospheric CO 2 changes when eccentricity is low. Therefore, in spite of the many uncertainties, we suggest that changes in CO 2 , rather than that of ice volume, are the primary driver of the phase modulation with the 400-kyr periodicity.
The phase modulation of CO 2 over a 400-kyr-long cycle is linked to the reduced amplitude of precession variations during periods of low eccentricity (Fig. 4h), which result in a relatively strong obliquity effect. During TI, CO 2 rose at~18 kyr BP, which is related to the melting of the Northern Hemisphere ice sheet and the subsequent weakening of the Atlantic meridional overturning circulation (AMOC) 11 . Thus, the timing at which CO 2 begins to rise during a termination would be determined by when the Northern Hemisphere ice sheet begins to melt. When eccentricity is small, the summer insolation maxima are small. Thus, if obliquity rises beyond the threshold of melting, a moderate climate forcing could cause warming enough that the southern margin of the North American ice sheet begin to retreat 41 . Therefore, from 350 to 450 kyr BP, the obliquity component of CO 2 began to rise rapidly without a phase difference relative to obliquity.
Besides the timing of deglaciation, the ca. 400-kyr long cycle of the global ocean carbon cycle may also modulate the phase relationship. A pronounced increase in coccolith production, which cause atmospheric CO 2 to increase, occurs at the time of low eccentricity 45 (Fig. 5e). Paradoxically, the amplitudes of changes in the atmospheric CO 2 records from ice cores remain relatively stable at that time (Fig. 5a), suggesting that the enhanced efflux of CO 2 may have been counterbalanced by high total marine productivity 46,47 , which would be linked with enhanced iron fertilization during MIS 8, 10 and 12 in the South Atlantic Ocean 48 (Fig. 5f). These data imply an irregular enhancement CO 2 exchange between the atmosphere and the ocean from 350 and 450 kyr BP, which would have contributed to the small amplitude of CO 2 variations in the obliquity band between 350 and 450 kyr BP.
We suggest that a reduction in the response time of the ocean to changes in solar insolation during the periods of low eccentricity may have produced the reduction in the phase difference between insolation forcing, ΔT site and ΔT source in the obliquity band. It has been suggested that, during glacial periods, carbon becomes sequestered in the deep Southern Ocean through reduced deep-water ventilation and enhanced nutrient utilization 10 . In fact, the intermediate-to-deep δ 13 C gradient in benthic foraminifera (Δδ 13 C), which is a proxy for deep-water ventilation in the South Atlantic Ocean, shows weaker deep-water ventilation during glacial times with a clear 100-kyr glacial cycle; 49 this gradient also displays a secular 400-500-kyr-long trend in the glacial minima from MIS 6 to MIS 14 (Fig. 5c). Further, the record of Δδ 13 C between the North Atlantic and the tropical Pacific Ocean, which is a measure of overturning strength, shows a similar secular trend, and the lowest Δδ 13 C value occurs during MIS 12 (Fig. 5d). These results imply a drastically reduced ventilation of the Atlantic or enhanced ventilation in the Pacific 50 . The above studies suggest that the deep ocean water was isolated from the surface-intermediate ocean during these periods because of weakened ocean circulation. The separation from the large heat reservoir of the deep oceans would have resulted in relatively fast thermal exchange between lower atmosphere and the surface ocean and a more rapid response of surface water temperatures to changes in insolation.
The reduced ventilation of the Atlantic (Fig. 5d) is linked with the exceptional cooling seen in ΔT source during MIS 12.2 (Fig. 3a). This exceptional cooling of the Southern Ocean temperatures was likely associated with anomalously cool tropical SSTs that occurred at that time and were caused by northward movement of the subtropical front (STF) 50 . The annual maximum and minimum of daily equatorial insolation has pronounced eccentricity periodicities 51 Fig. 4g). c The intermediate-to-deep δ 13 C gradient of benthic foraminifera (Δδ 13 C), a proxy for deep-water ventilation in the Southern Ocean 49 . Δδ 13 C represents the difference in δ 13 C between two cores, specifically those collected at ODP site 1088 (ca. 2100 m water depth) and site 1090 (ca. 3702 m water depth) in the South Atlantic Ocean. Dotted red line indicates the Δδ 13 C obtained using C. kullenbergi data at site 1090 and solid red line indicates C. wuellerstorfi data only. d A measure of overturning strength based on δ 13 C gradient 50 between the North Atlantic (ODP site 607) 91 and the tropical Pacific Ocean (ODP site 846) 92 . Small gradients (close to zero) imply drastically reduced ventilation of the Atlantic or enhanced ventilation in the Pacific 50 . e Sr/Ca of coccolithophores as a proxy for the rate of coccolithophore production in southwestern Indian Ocean (purple line, MD962077) and in the western equatorial Pacific (blue line, V28-239) 45 . Our temperature data reveal that the asynchrony between Antarctic temperature and CO 2 has been associated with obliquity over the past 720,000 years. Large obliquity-induced variations in AMI strongly affect Antarctic temperature. Moreover, this obliquity effect is modulated by the eccentricity periodicity. During periods of low eccentricity, the delayed responses of ΔT site , ΔT source and CO 2 relative to AMI are minimal in the obliquity band. One possible explanation for this phenomenon is that the secular changes in the global ocean carbon cycle affect changes in ice volume, particularly during eccentricity minima. The secular changes in ocean circulation result in the isolation of the large heat reservoir of the deep ocean, and contribute to the reduction in the phase difference between AMI, ΔT site and ΔT source in the obliquity band. The Earth's climate system is presently in a period of reduced eccentricity like the one that occurred at~400 kyr BP. In the absence of human activities, the decrease in obliquity (and thus AMI at high latitudes) during the next 10 kyr would cause temperatures on the East Antarctic Plateau to decrease by 1-2°C in the obliquity frequency band. The obliquity-paced solar radiation is also important as a driver of changes in glacier mass balance in Antarctica 52 . Thus, it is crucial to understand the climate mechanisms that underlie the apparent 400-kyr phase modulation of AMI relative to temperatures, CO 2 and ice volume.

Methods
Samples and isotope measurements. The DF2 ice core was drilled to near bedrock at a depth of 3035.2 m 53 at the DF station in East Antarctica. The drilling site is located at a summit of the East Antarctic ice sheet and has a current annual mean air temperature of −55°C. Extensive analyses of the deepest part of the ice (3000.0-3035.0 m) indicate that the bottom ice originated from meteoric water with altered chemical compositions 54 .
Measurements of δD and δ 18 O values were performed for 6349 samples, which were obtained at depths ranging from 2399.5 to 3035.0 m. Each sample was 10 cm in length, which corresponds to a mean temporal resolution of~70 yr. To remove surface contamination, 13 wt% of the surface was removed from each 24-g ice sample with a ceramic knife. The ice samples were melted at room temperature in sealed polyethylene bags. The water was then transferred to glass bottles and preserved in a frozen state. Both δD and δ 18 O values were measured using an automated equilibration method 55 20 . The sawdust was collected during ice cutting at the DF site. The average difference (=δ 18 O saw -δ 18 O ice ) and its variations (±1σ) were 0.31 ± 0.18‰ (n = 15), respectively. The small enrichment in δ 18 O saw was caused by sublimation during sampling and/or transport of the samples from Antarctica to Japan. In addition, the resolution of this study is five times higher than that of the 50-cm sampling used in the previous DF2 δ 18 O saw data 20 .
The isotope data are given using conventional δ notation: δ = R sample / R VSMOW −1, where R sample and R VSMOW are the isotopic ratios (D/H and 18  Combining the record and the time scale. To obtain a complete isotopic record over 720 kyr, we used published data sets from the first Dome Fuji (DF1) core for shallow depths ranging from 0.0 to 2399.5 m. For the portion of the record derived from the DF1 core 21,56-58 , the resolution was ca. 400 years, and some parts were discontinuous. The overlapping portion (2400-2500 m) of the DF1 and DF2 records exhibited remarkable similarity 22,59 because the horizontal distance between the two sites was only 43 m. The combined record was obtained by replacing the DF1 data [56][57][58] with the DF2 data within the depth interval where the two cores overlap 22 and adding the DF2 record. In this study, the DF records were plotted on the AICC2012 age scale 23,60 . To transfer the DF data to the AICC2012 age scale 23 , volcanic tie points between DF and EDC were used for 0-216 kyr BP 61 . For 216-720 kyr BP, the isotopic profiles were synchronized using the Match software package 62 . The glacial inceptions were excluded from the predetermined tie points 20 because of potential differences in the patterns of the two isotopic profiles 63 . The largest mismatch between DF2 and EDC was found during 600-610 kyr BP. Isotope matching was impossible for this part of the record because of substantial differences in the observed trends.
Temperature reconstruction. Traditionally, δD is used as a proxy for surface air temperatures, based on the spatial linear correlation between δD measurements and Antarctic temperatures 64 . However, the δD and δ 18 O variations in Antarctic ice cores 1,2 depend on the extent of fractionation-associated rainout from atmospheric water vapour along the pathway from the oceanic moisture source to the precipitation site, as well as the site temperature (ΔT site ). To estimate the site air temperature (ΔT site ), including a correction for the temperature of the moisture source regions (ΔT source ), a linear inversion method was used. This method has previously been applied to the Vostok core 18,29 , the EDC core 65 and the DF core 22 . The sensitivities of the δD and d values to DF site air temperatures (ΔT site ) and the temperatures within the moisture source region (ΔT source ) were estimated using a mixed cloud isotopic model 66 . The multiple linear regression is expressed using the following equations: where Δ represents the deviation from the modern (where the modern is defined as the average value for the past 2 kyr), and the subscript 'corr' indicates the ice core record corrected for the isotopic composition of ocean water (Δ 18 O sw ) 67 using the Rayleigh equation 68 . For the temperature sensitivity parameters, γ site , γ source , β site and β source , we used the values given by Uemura et al. 22 . Based on Monte Carlo simulations performed using the Vostok core, the uncertainties in the glacial-interglacial magnitudes of ΔT site and ΔT source are 1.1°C and 0.8°C, respectively 29 . The uncertainties for the DF site should be similar to those at Vostok because both are located in the inland portion of East Antarctica.
The above equations were written with a traditional linear definition of d to allow direct comparison with previous publications. Note that the definition of the d value does not affect the reconstructions for ΔT site and ΔT source values. Instead, it affects only the sensitivity parameters 22 . A comparison of the ΔT source , d and d ln shows that ΔT source resembles the variations in d ln more closely than those of d for glacial-interglacial cycles ( Supplementary Fig. 3).
In addition to ΔT source , relative humidity may affect the d values. In fact, present-day observations of water vapour in the Southern Ocean show that d depends on both SSTs and relative humidity 69 . Based on a Rayleigh-type model, the dependency of d on relative humidity has been estimated to be −0.15‰/% at Vostok 19 and −0.045 to −0.095‰/% in East Antarctica 70 . An atmospheric general circulation model does not produce significant changes in relative humidity between the present day and the last glacial period 71 . A state-of-the-art climate model that includes coupled atmosphere, ocean and land processes also revealed changes in relative humidity of only ±5% over the ocean surface in the Southern Hemisphere 72 . Based on this relative humidity estimate and the sensitivity values, the changes in relative humidity lead to changes in d of ±0.23 to ±0.75‰, which is not significant when compared with the ca. 6‰ amplitude of the glacial cycles ( Supplementary Fig. 3). Furthermore, general circulation models generally support the interpretation of ΔT source in Antarctica 73,74 .
SST records. In total, 17 SST records from ocean sediments 50,75-86 within the DF moisture source region (Fig. 1) were collected from published databases. Various proxies (alkenones, Mg/Ca and faunal) were used to reconstruct the SSTs within that region. Six of the profiles reflect annual mean SSTs, whereas nine of the profiles reflect summer SSTs. Two of the profiles were produced by averaging summer and winter SST records 85 . The SST values are expressed in terms of deviations from the modern value, ΔSST ( Supplementary Fig. 4), as with ΔT source . In this study, the average values for the past 2-5 kyr were used as the modern values. For MD07-3077, which does not contain data from the Holocene, modern SST data from the same site, MD07-3076, were used. In the case of MD02-2488, for which the SST data begin at 49 kyr BP, the present-day summer SST value was used as the modern value. Each ΔSST data series was resampled at a 2-kyr interval with linear interpolation. A stacked ΔSST record was then obtained by averaging the data without tuning the original age scales. The uncertainty in ΔSST was estimated by multiplying the standard error (σ/√n) by the t-value (97.5% confidence level). The stacked SST profile and uncertainty intervals are shown only for the period during which multiple data records (4 or more) were available ( Fig. 1 and Supplementary Fig. 4).
Albedo data. The albedo climatology was derived from data collected by the TIROS-N satellite. This data set was obtained from the climate data archive of the Joint Institute for the Study of the Atmosphere and Ocean (http://www.jisao. washington.edu/). The albedos of the DF region and the moisture source region are 0.78 and 0.46, respectively.
Significance of the correlation coefficient. The uncertainty of the linear correlation coefficient was estimated using the Fisher Z-transform. For the entire record, the 90% confidence ranges of the correlations (R 2 ) of CO 2 with δD, ΔT site and ΔT source are 0.68-0.73, 0.76-0.80 and 0.75-0.79, respectively. For the lukewarm period, the ranges of the correaltion of CO 2 with δD, ΔT site and ΔT source are 0.60-0.70, 0.72-0.79 and 0.77-0.83, respectively. Thus, the correlation between ΔT site (and ΔT source ) and CO 2 is significantly stronger than that between δD and CO 2 . The correlation between ΔT source and CO 2 is slightly higher than that between ΔT site and CO 2 , but it is statistically insignificant.
Spectral analyses and the obliquity component. Spectral analyses were conducted with the Blackman-Tukey method (30% lag) using the Analyseries software package 87 (Fig. 3 and Supplementary Fig. 5). The amplitudes of the records were normalized to a standard deviation of 1. The data shown in Fig. 3 were resampled using linear interpolation to a 700-yr interval, which is the average resolution of the composite CO 2 record, and then smoothed using a 1-kyr cutoff low-pass filter. The data in Fig. S5 were resampled using linear interpolation to a 100-yr interval. The insolation data 88 and the 41-kyr obliquity components (Fig. 4) were calculated using a Gaussian filter using the Analyseries software package (f = 0.0244 (1/kyr) with a bandwidth of 0.00488).
The uncertainties associated with the phase analysis were of three types: (i) ice-age versus ice-age phase analysis error (σ phs ). The relative lags between the temperature proxies were as reliable as possible because they were estimated from the same ice sample. The phase analysis between ΔT site and ΔT source ( Supplementary Fig. 5) is shown with a 90% confidence interval. (ii) Ice-age versus gas-age phase analysis error (σ CO2 ). Determining the exact phase lag between CO 2 concentrations and temperatures was complex because the air was younger than the surrounding ice. A phase analysis between the temperature proxies and CO 2 (Fig. 3) is shown with a 90% confidence interval (i.e. the error described in (i)) and an additional uncertainty associated with the gas-age/ice-age difference of ±0.55 kyr. This additional uncertainty was estimated using a gas-age/ice-age difference of 1.9-5.5 kyr 8 and a 10% uncertainty in the age difference 89 , which approximately doubled the analytical uncertainty of the phase between ΔT site and ΔT source . (iii) Ice-age versus orbital-age phase analysis error (σ orb ). To compare with the variation in obliquity, the absolute age uncertainty of AICC2012 for ice must be considered. The uncertainty of AICC2012 is ±2.6 kyr on average during the past 100-720 kyr 23 . The phase lag and confidence intervals (90%) of ΔT site , ΔT source and ΔT grad with respect to obliquity were 4.1 ± 0.7, 7.5 ± 1.3 and 1.9 ± 0.3 kyr, respectively. For example, a combined error estimate for ΔT site that is based on the root mean squared error is ±2.7 kyr. Therefore, the 4.1-kyr lag of ΔT site against obliquity was significant during most of the studied period. The error in the gas-age versus orbital-age phase analysis is similar to σ orb because the uncertainty of the AICC2012 age scale for gas is ±2.6 kyr, on average, during the past 100-720 kyr 23 .