First, we investigate whether the SPICEcore ΔTz reconstruction can be explained by variations in surface temperature. Changes in mean annual site temperature affect the firn temperature difference as the surface snow warms or cools and the vertical temperature profile in the ice sheet adjusts to a new equilibrium. Surface temperature change might also explain the negative relationship between DCH and ΔTz in our data, with a surface cooling trend typically resulting in a more negative ΔTz and a thicker firn column via reduced densification rates (Herron and Langway, 1980). We estimate the surface temperature history using the dynamical firn densification–heat transport model (Sect. 3.3) in an inverse mode. Briefly, the model adjusts initial estimates of past surface temperature and accumulation rate to best fit proxy-based reconstructions of firn thickness and gas age–ice age difference (Δage). This REF model run is able to produce a good fit to the proxy-based estimates of firn thickness and Δage for SPICEcore (Buizert et al., 2021) and also agrees well with our estimates of DCH and ΔTz for much of the last glacial and Holocene periods (Fig. 4). However, the modeled ΔTz from the REF run does not agree well with our ΔTz reconstruction during the LGM and for much of the deglaciation. The model does not reproduce the most negative values of ΔTz between 23 and 18.5 kyr BP, nor does it capture some of the most positive values between 8.5 and 6.5 kyr BP. The firn model is not capable of fitting the ΔTz data while simultaneously fitting the observational DCH and Δage data.

To evaluate what temperature history would be required to fit the ΔTz data, we perform an additional experiment in which the firn temperature is decoupled from the firn densification physics (we call this the DECOUPLE run). In the DECOUPLE run the firn densification rates are not calculated, but rather they are read out from a data file corresponding to the densification rates from the REF experiments. Accumulation rates are likewise equal to those from the REF run. The inverse model is then tasked to reconstruct the surface temperature history that best fits the ΔTz data. The DECOUPLE surface temperature history required to fit our ΔTz data is show in Fig. 4. Note that the DECOUPLE scenario is not internally consistent as the firn densification rates are inconsistent with the temperature forcing used. The design of the DECOUPLE experiment simply allows us to control the thermal gradient in the firn column (and thus ΔTz) while simultaneously ensuring we use the correct firn thickness and rate of downward advection of ice and heat.

We focus our interpretation of the DECOUPLE simulation on the direction and timing of changes in the inferred temperature history, rather than the absolute values, as ΔTz is more sensitive to changes in surface temperature than to the temperature itself. Also shown for comparison is the optimal temperature history from the REF run (Buizert et al., 2021) and a temperature history from Kahle et al. (2021) based on a calibration of δ18Oice using the SPICEcore Δage data and the diffusion length of water isotopes in the firn. Note that both temperature histories are partially constrained by the Δage data, so they are not wholly independent.

The DECOUPLE temperature history differs substantially from the other temperature estimates. It features a prolonged 5 ∘C cooling between 23 and 20 kyr BP, followed by a rapid 5 ∘C warming from 13 to 11 kyr BP. The cooling event in the decoupled temperature history happens at a time when the other estimates indicate either constant temperatures or a slight warming associated with the initiation of the deglaciation, whereas the decoupled history shows almost no warming until the deglacial temperature change is almost fully realized in the other estimates. The timing and sign of temperature changes in the decoupled temperature history also bear little resemblance to other Antarctic ice core temperature reconstructions (Buizert et al., 2021; Uemura et al., 2018; Cuffey et al., 2016; Stenni et al., 2011; Jouzel et al., 2007; Petit et al., 1999).

Based on both the poor agreement of the measured and modeled ΔTz in the REF run and the poor agreement of the DECOUPLE temperature history with other reconstructions, we conclude that surface temperature change is unlikely to fully explain our record of ΔTz, particularly the most negative values at 20 kyr BP.

Second, we investigate whether the SPICEcore ΔTz reconstruction may be explained through variations in the thickness of the ice sheet. Ice thickness influences ΔTz by controlling the vertical strain rate in the ice sheet and thereby the downward advection of cold ice and the ability of geothermal heat to warm the base of the firn column. Temporal changes in ice thickness over the course of our record are certainly plausible, especially given that the flank location of the South Pole means older ice originated upstream from the present-day SPICEcore site. The relevant parameter for our record of ΔTz is the thickness of the ice column at the time and location that the bubbles were occluded. Variations in ice thickness experienced by SPICEcore ice are therefore the result of both temporal fluctuations in ice sheet elevation and upstream spatial fluctuations in ice thickness.

Temporal changes in ice sheet elevation at the South Pole were estimated by Fudge et al. (2020) using output from a full ice sheet model from Pollard et al. (2016). They conclude that changes in ice thickness have most likely been smaller than ±100 m in the past 20 kyr, with a mean elevation change of +16 m at 20 kyr BP. Certain combinations of model parameter values give changes between -325 and +250 m. Outside of the Holocene, the rate of change is always less than 20 m kyr-1.

Spatial changes in ice thickness upstream of the SPICEcore site are dominated by changes in bed topography. For the Holocene, changes are well-known as the flowline is tightly constrained for this time period and the bed topography has been determined by ice penetrating radar (Lilien et al., 2018). Fluctuations are smaller than ±250 m. Beyond the Holocene, estimates of the bed topography do exist, but the exact flowline position becomes increasingly uncertain. Kahle et al. (2021) offer some constraints from their estimate of the SPICEcore thinning function and infer possible changes in bed elevation of around +200 m between 33 and 26 kyr BP and -200 m between 23 and 18.5 kyr BP.

We therefore seek to determine the maximum plausible change in ΔTz by simulating a 500 m thickening or thinning using a one-dimensional ice flow model (Fudge et al., 2019). A 500 m change is 80 m larger than the range of present-day ice thickness fluctuations in the 100 km upstream of the SPICEcore site, corresponding to the past 20–25 kyr (Lilien et al., 2018); it is more than twice the magnitude of the changes in bed topography inferred by Kahle et al. (2021) in the past 30 kyr BP, and it is 1.5 to 2 times larger than the most extreme modeled surface elevation changes in the past 20 kyr. In our experiments, the modeled changes in ice thickness occur linearly over 2000 years, and the post-change thickness is set to the present-day value of 2800 m in each case. We repeat each experiment twice with accumulation rates of 2 and 4 cm yr-1.

The results of these simulations are shown in Fig. 5. The thinning (thickening) experiments result in a decrease (increase) in ΔTz to more (less) negative values. Lower accumulation rates correspond to more negative values of ΔTz due to weaker downward advection of surface heat. The change in ΔTz is less than 1 ∘C for each experiment – 3 times smaller than the largest change in our record. We therefore conclude that fluctuations in ice thickness are also unable to fully explain our observations.

Third, we investigate whether the SPICEcore ΔTz reconstruction may be explained through variations in the basal geothermal heat flux (GHF). As discussed above, most East Antarctic ice cores have negative values of ΔTz caused by geothermal heat impinging on the base of the firn column due to low accumulation rates at these sites. Although the GHF at the South Pole is constrained by borehole temperature measurements (Price et al., 2002; Beem et al., 2018), the firn temperature gradient at 20 kyr BP may have been set by very different basal conditions as the ice sheet flowed over regions of greater or lesser GHF towards the present-day SPICEcore site. In fact, a recent survey upstream of the SPICEcore site inferred values as high as 120 W m-2 due to local faulting and hydrothermal activity (Jordan et al., 2018), more than double previous estimates for the region from continent-scale models (Van Liefferinge and Pattyn, 2013).

To test the hypothesis that the most negative values of ΔTz and the negative relationship between DCH and ΔTz are the result of spatiotemporal variations in GHF, we simulate the effect of a step change in the GHF using the firn densification model described in Sect. 3.3. To calculate an upper bound on the plausible change in ΔTz, we choose a low starting value of 40 W m-2 and either double or triple the GHF instantaneously. We repeat the experiments with three difference ice thicknesses: 2800, 2300, and 1500 m. The first represents the present-day ice thickness at the South Pole, and the second represents a plausibly thinner ice sheet (as deduced in Sect. 5.2.2). The third is a more extreme scenario, representing the minimum observed thickness in a recent survey of the upstream region (Beem et al., 2021). For all experiments, the accumulation rate is 4 cm yr-1, and the surface temperature is -58 ∘C, representing LGM conditions.

The results of the model experiments are shown in Fig. 6. Over the course of ∼ 100 kyr, the firn temperature profile adjusts to the new steady state, with ΔTz decreasing by 0.7–2.9 ∘C, depending on the ice thickness and GHF change. However, in our record of ΔTz, variability of this magnitude occurs in ∼ 5 kyr. The model indicates that GHF changes can explain < 0.5 ∘C of change in ΔTz on this timescale and only under the most extreme case of a tripling of GHF with a 1500 m ice column. Furthermore, a larger GHF would likely result in a slightly smaller DCH as the warmer firn column would densify more rapidly. This prediction is confirmed by the model (not shown) and is opposite to the inverse relationship we observe between DCH and ΔTz. Therefore, we conclude that spatial variability in the GHF upstream of the South Pole is unable to fully explain our observations, particularly the rapid 3 ∘C changes in ΔTz between 23 and 18.5 kyr BP.

Last, we investigate whether the SPICEcore ΔTz reconstruction may be explained through so-called rectifier effects. Based on the evidence presented in previous sections, we argue that none of the processes known to control the annual-mean firn temperature profile can adequately explain our ΔTz observations in terms of their magnitude, rate of change, and inverse relationship with DCH. Notably, however, temperature differences much larger than -4 ∘C do arise on sub-annual timescales within the upper 20 m of the firn, at the South Pole and elsewhere, in response to the seasonal surface temperature cycle (Dalrymple et al., 1966; Severinghaus et al., 2001; Brandt and Warren, 1997; Town et al., 2008). The corresponding gas isotope thermal fractionation signals only penetrate to ∼ 10–15 m depth (Severinghaus et al., 2001; Weiler et al., 2009) and are typically assumed to cancel out each year such that the deep firn (and thus the ice core gas archive) reflects the annual mean. Although existing firn air data from multiple sites are largely consistent with this assumption, the data are often lower precision than our measurements and are unlikely to represent a complete picture of firn processes on the spatial and temporal scales captured by our ice core record. Therefore, because annual-mean processes are unable to explain our data, we now investigate the possibility that some values of ΔTz in our SPICEcore record could be the result of isotope signals in the deep firn being biased towards a particular season at certain times in the past. During winter, cold surface ice overlays a warmer firn column producing negative ΔTz values in the upper firn, and vice versa during summer. To explain the most negative values of ΔTz between 23 and 18.5 kyr BP, we infer a wintertime bias that is either weaker or non-existent at other times in the record. In addition, we propose that the most positive values between 8.5 and 6.5 kyr BP may represent a summertime bias. One notable aspect of this mechanism is that its strength can change very quickly – firn air convection appears and disappears on seasonal timescales. This may help to explain the changes in ΔTz we observe between 23 and 18.5 kyr BP that are either too large or too abrupt to be explained by the processes discussed in previous sections.

In the sections below, we discuss mechanisms that might produce a summer or winter bias and argue that this hypothesis can explain many features of our dataset, including the most negative values of ΔTz, the rate at which they develop, and the inverse relationship between ΔTz and DCH.

Seasonal isotopic thermal fractionation signals in the firn are typically overwritten by the opposite signal of the following season (Severinghaus et al., 2001; Weiler et al., 2009). One way a seasonal bias can develop in the deep firn is if one season's isotope signal is preferentially preserved by being advected down into the firn, below the depth to which the next season's diffusive isotope signal penetrates. This type of differential preservation of winter versus summer signals due to covariation of gas transport and concentration has been called a “seasonal rectifier effect” in prior literature (Denning et al., 1995; Severinghaus et al., 2001, 2010; Dreyfus et al., 2010; Trudinger et al., 2020). We adopt this language here.

This type of rectification requires a slow, non-turbulent, downward movement of air that occurs during one season but not the other. A plausible driving mechanism is the snow temperature inversion that arises in winter. Because snow and firn are efficient emitters in the infrared band and are usually warmed from below, their temperature is often coldest at the surface. This is especially true in winter when incoming solar radiation is reduced or even absent. The temperature inversion results in an unstable air density profile in the firn that can trigger buoyancy-driven Rayleigh–Bénard convection, thus advecting seasonal isotope signals deeper into the firn. In this section we discuss evidence for this type of air movement in snow and firn and investigate its ability to explain our SPICEcore gas isotope records.

Sturm and Johnson (1991) demonstrated that buoyancy-driven overturning occurs readily in sub-Arctic snow in Alaska. By making hourly observations of the three-dimensional temperature field within the winter snowpack for 3 years, they were able to observe large horizontal temperature gradients within the snow that were initiated and maintained by columns of rising warm air and sinking cold air. This convection occurred almost continuously throughout two successive winters. There is also ample evidence for air circulation within snow and firn from Antarctica, particularly if vertical cracks allow for fast upward return flow (Giovinetto, 1963; Albert et al., 2004; Fahnestock et al., 2004; Courville et al., 2007; Severinghaus et al., 2010). Unfortunately, direct observations of changes in firn air composition associated with convection are scant since firn air sampling happens almost exclusively in the summer. However, there are published data from a winter firn air sampling campaign at the South Pole. In this case, the authors did indeed find that the peak wintertime isotope signal occurred deeper than their firn air model predicted and speculated that this could be due to downward transport of the isotope anomaly by slowly sinking air (Severinghaus et al., 2001). If correct, this would provide confirmation not only of wintertime convection at the South Pole but also that thermal isotope signals can be carried down into the firn by convection without being destroyed by turbulent mixing.

To test their hypothesis, we compare their wintertime firn air measurements from the South Pole with values predicted by firn air model runs with and without parameterized Rayleigh–Bénard convection (Fig. 7). In the model run without convection, the gases diffuse towards gravitational and thermal equilibrium as they are slowly advected downwards with the densifying firn and occluded in bubbles in the lock-in zone. Because the model is one-dimensional, it is not possible to explicitly simulate a three-dimensional Rayleigh–Bénard convection cell. Instead, we model just the sinking core of a convection cell, which we parameterize as an 8 cm d-1 downward transport of gas between 0 and 20 m. Between 20 and 25 m, the downward transport decays to zero, resulting in mass convergence that would be balanced in the real world by horizontal transport and a return flux of gas to the surface. This approach allows us to approximate how the gas isotopes respond to convection using a one-dimensional model. The model run with downward transport agrees better with the observed wintertime firn air isotope ratios, with the negative wintertime values occurring deeper in the firn than in the model run with no downward advection. The model and the data therefore support our hypothesis that convection can carry seasonal thermal isotope signals down into the firn.

Because isotope data are only available in the top 16 m of the firn, we do not have an observational constraint on the strength of rectification in the deep firn where ice core signals are recorded. To demonstrate that seasonal convection can affect isotope values in the deep firn, we perform an additional experiment with the firn air model. We simulate the isotope values in the full firn column under idealized South-Pole-like conditions (110 m thick firn, -51 ∘C annual-mean temperature, 7 cm yr-1 accumulation) and impose a 14 cm d-1 downward advection throughout winter (April–September). In the model, the wintertime signal is advected deeper than the summer signal and so is not fully canceled out. This results in a -0.008 ‰ bias in the annual-mean signal in the deep firn compared to the control run with no downward advection (Fig. 8, Movie S1 in the Supplement). The bias is of comparable magnitude to the signals in our SPICEcore record, demonstrating that this mechanism could plausibly explain some of the millennial variability we observe.

To explain the correlation between DCH and ΔTz in our SPICEcore record, the strength of the wintertime convection must be linked to the wind speed and/or the topographic slope such that the rectifier is strongest when DCH is also at its maximum. We hypothesize that this link is provided by the energy balance at the snow surface. Stronger katabatic winds on steeper slopes weaken the air temperature inversion by turbulently mixing heat down to the surface from aloft (Hudson and Brandt, 2005; Pietroni et al., 2014). The opposite is true in areas of minimal slope: weaker winds allow a strong inversion to develop via efficient loss of infrared radiation to space from the surface snow. This intense cooling of the surface promotes convection in the firn (Sturm and Johnson, 1991), which would strengthen the wintertime bias. Low wind speeds probably also limit the formation of low-permeability wind crusts that would inhibit convection (Domine et al., 2018). By this mechanism, the wintertime bias would be strongest and ΔTz most negative in areas of flat topography, as we observe in our SPICEcore record (Fig. 3).

As further evidence for this type of seasonal rectifier, we also present a previously unpublished ΔTz record from the Dome Fuji ice core. The core was drilled in 1994–1996, and samples were stored at -50 ∘C until they were analyzed at Scripps Institution of Oceanography in 2007 using a different method to our SPICEcore dataset (Bereiter et al., 2018). Briefly, an ice sample of 800–900 g was melted in an evacuated vessel, and the released air was continuously transferred to a dip tube through a -100 ∘C water trap while stirring the meltwater. The air sample was split in two aliquots (Method 1 in Bereiter et al., 2018): one was measured with Thermo Delta-Plus XP for δ15N, and the other was gettered to extract noble gases and then measured with Thermo Finnigan MAT 252 for δ40Ar. The isotope data and the reconstructed ΔTz data are shown in Fig. 9, and we compare them to our estimate of the modeled Holocene ΔTz from Buizert et al. (2021). The model estimate is based on the same firn densification modeling approach described in Sect. 3.3 and constrained by Dome Fuji δ15N and empirical Δage datasets described in Buizert et al. (2021). To estimate the uncertainty in the modeled ΔTz, we re-run the model with different values of the GHF and accumulation rate. We change the GHF by ±10 W m-2 and the accumulation rate by ±10 %. The total uncertainty we report is the quadrature sum of the difference between these model runs and the optimal scenario.

Just like the SPICEcore record, the Dome Fuji ΔTz data show evidence of a wintertime bias due to rectification. The mean of the Holocene ΔTz data is more negative than both the present-day ΔTz and the modeled Holocene ΔTz. Large changes in surface temperature, ice thickness, and GHF can be excluded during the Holocene, so we conclude that the mismatch is most likely due to rectification producing a wintertime bias throughout the Holocene at Dome Fuji. Because katabatic winds are weak at ice domes due to the flat topography, we expect that the wintertime Rayleigh–Bénard rectifier would be particularly effective at this site. This finding strengthens the case for the existence of rectification in Antarctica and demonstrates that rectification can affect gas records at both dome and flank sites and over a wide range of site characteristics (Dome Fuji is 1000 m higher in elevation, is 5 ∘C colder, and receives half as much snow accumulation).

Also plotted is the ΔTz calculated from δ15N and δ40Ar measurements on firn air collected at Dome Fuji in 1998, which is -1.2 ∘C (Fig. 9, Sect. S3.2). This is more positive than the Holocene ice data and is consistent with the present-day observed firn temperature profile, suggesting no winter rectification is necessary to explain current conditions at Dome Fuji. This could be due to the cessation of rectification at some time during the past 2000 years, perhaps in the last century due to anthropogenic warming (the ice surface absorbs downwelling longwave radiation from greenhouse gases very effectively).

In summary, we propose that low wind speeds over areas of minimal topographic slope cause surface snow temperatures to be colder than on steeper slopes. In winter, this can result in an unstable air density profile in the firn and slow, non-turbulent convection of air to a depth of 10–20 m. This is deep enough to produce a cold, wintertime bias in our ice core records of ΔTz. In the Dome Fuji ice core, this bias existed throughout the Holocene until at least 2 kyr BP, whereas in SPICEcore, the cold bias is strongest at 20 kyr BP and is co-located with a thicker firn column due to the increased net accumulation of snow associated with slower and/or decelerating winds. Although this hypothesis is somewhat speculative, we believe this mechanism can plausibly explain (i) the most negative values in our record of ΔTz, (ii) the observed rate of change in ΔTz, and (iii) the inverse relationship with DCH.

The slow, non-turbulent air circulation described above results in a wintertime bias in the deep firn. However, some sites in Antarctica experience vigorous turbulent mixing in the upper few meters of the firn column – termed the convective zone (Sowers et al., 1992; Bender et al., 1994; Kawamura et al., 2006; Severinghaus et al., 2010). This convective mixing of the free atmosphere into the surface firn “resets” the air composition back to atmospheric values, eroding the seasonal, gas isotope thermal fractionation signals. The depth and extent of the mixing is controlled in part by the surface wind speed, with deeper convection associated with faster winds (Kawamura et al., 2006). Because katabatic winds are generally stronger in winter (van den Broeke and van Lipzig, 2003), we propose that a summer bias in ΔTz could originate via a seasonality in the strength of convective mixing in the firn. We might expect stronger wintertime winds to be more effective than summertime winds at eroding the thermal signals in the upper firn, meaning the summertime thermal signal would be preferentially preserved in the deep firn.

Again, we test the plausibility of this hypothesis with the firn air model. For this experiment, we parameterize the convective zone as an eddy diffusivity term in the upper 10 m of the firn that varies seasonally in magnitude – the eddy diffusivity is 5 times larger in winter than in summer. This dampens the wintertime thermal isotope signal, meaning the summer signal is preferentially preserved, resulting in a +0.008 ‰ bias in the annual-mean signal in the deep firn compared to the control run with no seasonal change in the eddy diffusivity (Fig. 10, Movie S2). Again, the bias is of comparable magnitude to the signals in our SPICEcore record, demonstrating that this mechanism could plausibly explain some of the millennial variability we observe.

The summertime bias hypothesis is consistent with our SPICEcore data in that it predicts a deeper, stronger convective zone on the steeper slopes ∼ 50 km upstream of the SPICEcore site, where wintertime katabatic wind speeds would be faster (Vihma et al., 2011). This would produce a stronger, more positive bias in this location, potentially explaining the occurrence of positive values of ΔTz (Fig. 3). Although previous authors have speculated that this type of rectification could affect firn and ice core gas records (Severinghaus et al., 2001, 2010; Dreyfus et al., 2010; Petrenko et al., 2013; Verhulst, 2014), observational evidence is limited to one potential site (Law Dome, Antarctica; Trudinger et al., 2020). Future firn air campaigns may help to uncover additional evidence of rectification via seasonal variability in convective strength.