The COLDEX study area is divided into three regions based loosely on the ice thickness and its variability (Fig. 2):

Foothills – upstream-most portion of the survey towards Dome A with variable ice thickness that typically ranges from ∼2500 to ∼3000 m.

We use a one-dimensional, steady state ice and heat flow model to calculate the temperature and age of ice with respect to depth. The age model is identical to that in Bereiter et al. (2014). The temperature model differs in that we utilize a temperature dependent thermal conductivity and specific heat capacity, rather than an ice column average. If the basal temperature exceeds the pressure melting point, the melt rate is calculated. We choose a steady-state model because the conditions near the base of the ice sheet, where the vast majority of diffusion occurs, are relatively insensitive to the transient surface climate forcing. In a set of ice flow model runs, glacial-interglacial changes in surface temperature of 8 °C results in a difference in basal temperature of <0.5 °C (Buizert et al., 2021). This model utilizes input parameters of accumulation rate, ice thickness, surface temperature, GHF, and a parameter for the vertical deformation profile (Lliboutry, 1979). Figure 3a–d show an example output of this model using forcings of 2 cm yr⁻¹ accumulation rate, 3000 m ice thickness, -60 °C surface temperature, 50 m W m⁻² GHF, and a vertical deformation parameter of p=4.

The steady heat equation, following Firestone et al. (1990), is solved to obtain the vertical temperature profile: 1∂2T∂z2-w(z)κ∂T∂z=0, where T is temperature, z is height above the bed. The thermal diffusivity is given by κ=Kρc, where ρ is the constant firn column density based on South Pole values (Lilien et al., 2018), c is the temperature-dependent specific heat capacity given by Cuffey and Paterson (2010; Eq. 9.1), and k is the thermal conductivity exponentially fit to the Waite et al. (2006) data as described in the supplementary information of Buizert et al. (2021) (Specific values can be found in the setup_thermal_herc.m file in the GitHub repository). w is the vertical velocity as calculated by Parrenin et al. (2007): 2w(z)=-(A-m)ψ(z)m,3ψ(z)=1-p+2p+11-zH+1p+11-zHp+2, where A is accumulation rate, H is ice thickness, and p is a tuning parameter for vertical deformation (Lliboutry, 1979). The deformation parameter is assumed to be p=4 in all scenarios, unless otherwise stated. We include the bedrock in the thermal calculation and set the GHF at 7 km below the ice surface. The melt rate, m, is first set at 0 for calculating the temperature profile. Equation (1) is solved similarly to Firestone et al. (1990) with an integration factor: 4F(z)=exp⁡-∫0zw(ζ)κdζ. This gives the following solution: 5T(z)=TS-QK∫Hz1F(η)dη. where TS is the surface temperature and Q is GHF. The melt rate is calculated from the excess geothermal heat that the ice cannot conduct away from the bed. This is calculated iteratively because the melt rate affects the vertical velocity (Eq. 2) and thus the englacial temperature profile. The GHF is equal to the heat conduction through the basal ice and the latent heat lost in melting, which we assume is lost as the water flows away from the bed. The example temperature profile in Fig. 3a shows how temperature increases roughly linearly with depth approaching the bed as a result of this solution.

The vertical age profile is found by solving Eqs. (2) and (3) with the inferred melt rate and integrating the inverse of the negative vertical velocity: 6age(z)=∫-1w(z′)dz′. The example age-depth profile in Fig. 3b shows how the age of ice evolves with depth up to 2 Ma, after which older ice has been melted by the warm temperatures shown in Fig. 3a.

The gas diffusion model uses the temperature- and age-depth profiles described above to calculate the rate of diffusion through time (Ikeda-Fukazawa et al., 2005; Bereiter et al. 2014). Vertical gas diffusion is modeled as follows: 7∂Cn∂t=∂∂zDn∂Cn∂z, where Cn is the concentration in the ice of n (CO₂ or O₂) and Dn is the diffusion coefficient in ice. Gas exchange with surrounding ice is calculated according to Ikeda-Fukazawa et al. (2005) and Bereiter et al. (2009). The model does not include a portion for diffusion in bubbly ice and instead treats the whole ice column as clathrate ice for simplicity. While diffusion does occur within bubbly ice, the time gases spend in the bubble phase is relatively short compared to the timescales of interest here (e.g. ice 1000 m below the surface at EDC is ∼65 ka, roughly the extent of bubbly ice; Bazin et al., 2013; Veres et al., 2013). We only simulate the diffusion of O₂ because N₂ has a permeation coefficient roughly one order of magnitude lower than that of O₂ (Salamatin et al., 2001). Modeling O₂ diffusion is sufficient for modeling the damping of the O₂ / N₂ ratio. Including N₂ diffusion would reduce the smoothing of δO₂ / N₂ from O₂ diffusion, provided that the gas concentration gradient of N₂ has the same sign as O₂. This condition is likely met as millennial-scale variable of δO₂ / N₂ and total air content in ice is thought to be driven by similar bubble-closure processes. This is supported by empirical data showing δO₂ / N₂ and total air content covariance (Fujita et al., 2009; Lipenkov et al., 2011). Thus, this study provides an upper limit on δO₂ / N₂ smoothing in ice cores. Note that if O₂ and N₂ gas concentration gradients were of opposite signs, the effects of their diffusion would be additive and thus enhance smoothing.

The concentration of dissolved molecules of gas in pure clathrate ice, Cn, is calculated as follows: 8Cn=Zn⋅Pnd⋅Sn, where Zn is the molar fraction of gas n in air enclosed in the clathrate, Pnd is the clathrate dissociation pressure of gas n, and Sn is the solubility of gas n. The clathrate dissociation pressure is species and temperature dependent, and has been experimentally determined (O₂: Kuhs et al., 2000; CO₂: Miller, 1961). 9log⁡10Pnd=an-bnT, where T is the temperature in Kelvin.

After Bereiter et al. (2014), we use solubility and diffusivity parametrizations from Ahn et al. (2008) and Salamatin et al. (2001) for CO₂ and O₂, respectively. Diffusive smoothing is dependent on the product of diffusivity and solubility: permeability. Permeability values in clathrate ice are difficult to measure in a lab setting due to their extremely small values, so they are instead indirectly estimated based on a model which simulates air fractionation and diffusive smoothing in an ice core. The coefficients for CO₂ have experimental support at 250 K and are further extrapolated (Ahn et al., 2008). This is the only reliable estimate available for CO₂ permeability, based on an analysis of refrozen melt water in the Siple Dome ice core; however, these estimates have not been independently experimentally verified. Bereiter et al. (2014) modeled O₂ / N₂ diffusion under two sets of gas parameters, a “fast set” and “slow set”. The “slow set” parameters are derived from empirical fits to ice core data (Salamatin et al, 2001). The “fast set” parameters are based purely on molecular dynamics simulations of gas diffusion in ice (Ikeda-Fukazawa et al., 2004). The values for the “fast set” and the “slow set”, as well as for CO₂ permeability, can be found in Fig. S1 in the Supplement. Oyabu et al. (2021) demonstrates that the “fast set” parameters yield unrealistically high rates of smoothing compared to high resolution O₂ / N₂ measurements from the Dome Fuji core (DF1). Thus, we utilize the “slow set” in this study. For all gases, the permeation coefficients increase as temperature increases, with O₂ increasing more rapidly than CO₂, but their true sensitivity to temperature is not well known.

Within the gas diffusion model, we calculate the diffusivity as follows: 10Dn(T)=Dn0exp⁡-QnR⋅T, where Qn is the activation energy for the diffusion coefficient of molecules of gas n in ice Dn(T), R is the ideal gas constant, T is the temperature, and Dn0 is a specific constant for each gas (Bereiter et al., 2009; Ikeda-Fukazawa et al., 2005). For CO₂, we calculate solubility as follows: 11SCO2(T)=SCO20exp⁡-ECO2R⋅T, where ECO2 is the activation energy for the temperature dependent solubility SCO2(T) and SCO20 is a specific constant (Bereiter et al., 2009). To calculate solubility for O₂, we first calculate the permeability: 12PO2(T)=PO20exp⁡-QPR⋅T/Pdiss220K, where QP is the activation energy for permeation, PO20 is a specific constant (Salamatin et al., 2001), and Pdiss220K is the dissociation pressure of O₂ evaluated at 220 K, as in Eq. (9). Solubility is then solved as the quotient of the permeability and diffusivity.

The ice column is partitioned into discrete intervals of 50 kyr of ice age. An ice particle being advected down the ice column spends 50 kyr in each interval. An average annual layer thickness and average temperature are calculated for each interval. Gas concentrations are initialized, and the model simulates diffusion based on the properties of the first 50 kyr interval. Next, gas concentrations are saved, and the model physical parameters are updated using the average layer thickness and temperature from the next interval. Then, the simulation continues for the next 50 kyr interval. The process iterates until the last interval is reached (e.g. Fig. 3e and f).

We use a 40 kyr period for CO₂ to match the predicted frequency of glacial cycles prior to the MPT and a 20 kyr period for the O₂ / N₂ ratio to match precession cycles. To express the amount of signal amplitude lost to diffusion, we define the signal damping ratio (SDR) as: 13SDR(age)=1-X(age)X(0), where X(age) is the gas signal amplitude at a given age and X(0) is the initial gas signal amplitude. We use an initial amplitude of 50 ppm for CO₂ and 5 ‰ for the O₂ / N₂ ratio. The SDR gives the fraction of gas signal lost at a target age, with higher values indicating more diffused gas signals. The SDR for 1.5 Ma will be of most interest in this study as it fully covers the MPT and some time prior to it. Figure 3e and f shows how CO₂ and O₂ / N₂ ratio concentrations evolve through time given the corresponding temperature- and age- depth profiles. CO₂ signal amplitudes do not change significantly in this example (Fig. 3e). O₂ / N₂ ratio signal amplitudes dampen in old ice, particular in ice older than 0.9 Ma (Fig. 3f).

To determine the extent to which ice core gas concentration measurements can be used to estimate the expected diffusion of atmospheric gases in 1.5 Ma ice, we conduct four model runs. In the first run, we simulate the conditions for EPICA Dome C (EDC) and use parameter values from Bereiter et al. (2014) (“EDC” in Table 1). In the second run, we simulate the conditions for Dome Fuji with parameters values tuned to fit the age (Uemura et al., 2018) and borehole temperature data (Buizert et al., 2021) (“DF” in Table 1). We conduct two additional synthetic cases studies. The first synthetic case is an idealized scenario where diffusion is limited in 1.5 Ma ice (“Low diffusion” in Table 1). The second case aims to simulate a scenario with higher diffusive smoothing (“High diffusion” in Table 1). Figure 4 shows how the SDR of CO₂ and the O₂ / N₂ ratio evolve for each model run. The simulation of CO₂ smoothing at EDC yields an SDR of <0.1 % and an O₂ / N₂ SDR of 3 % at 0.8 Ma, the ice core record limit. The simulation of CO₂ smoothing at Dome F yields an SDR of <0.1 % and an O₂ / N₂ SDR of 2.7 % at 0.75 Ma, the age limit in the model run. Both the low and high diffusion model runs also produce SDRs for each gas below 10 % at 0.8 Ma, indicating that gas signal diffusion within the age range of the current ice core record is minimal. However, the SDR values between the low and high diffusion model runs diverge after 0.8 Ma, with the high smoothing simulation yielding an SDR of 84 % for O₂ / N₂ at 1.5 Ma and the low smoothing simulation yielding an SDR of 45 % at the same age. While atmospheric signals are well preserved in the ice sheet to 0.8 Ma, they may be significantly smoothed by 1.5 Ma. The simulated smoothing in ice older than 0.8 Ma is driven by extreme layer thinning and warmer temperatures near the bed. It will be important to consider gas diffusion in older ice despite the lack of diffusion in the current record as orbital scale variations in gases in the current ice core record cannot be used to estimate diffusion.

Here, we investigate the sensitivity of gas diffusion to four input parameters to the models: accumulation rate, ice thickness, surface temperature, and GHF. We hold three parameters constant and vary the fourth to gain an intuition for how SDR responds to each forcing parameter separately. Parameter values are chosen to keep the melt rate at zero. This ensures that the oldest ages are represented in this analysis and not destroyed by basal melt. The parameter values also are different between the CO₂ and the O₂ / N₂ ratio model runs. We consider separate sets of parameters for CO₂ and O₂ / N₂ because of the large difference in the diffusion rates of CO₂ and the O₂ / N₂ ratio. Fixed parameter values for each gas are shown in Table 2. The range for each variable parameter is based on the physical properties of the study area. The effects of the parameters are interrelated. For example, the effect of varying accumulation depends on the assumed temperature, ice sheet thickness, and GHF. So, this analysis should be considered qualitative. Figures 5 and 6 show CO₂ and the O₂ / N₂ ratio SDR sensitivity to input parameters.

The SDR of CO₂ increases roughly linearly with accumulation rate, surface temperature, and GHF, and decreases with ice thickness. Increasing accumulation yields increased SDR (Fig. 5a). Higher accumulation enhances signal smoothing because the thinner layers near the bed cause steeper gas concentration gradients. The steep gradients increase diffusion more than the decrease in ice temperature from greater vertical advection of cold surface temperatures. Additionally, the relatively steep slope in Fig. 5a shows that accumulation rate has the largest impact on CO₂ signal preservation. The effect of surface temperature and GHF are simpler. Lower values reduce SDR because of colder temperatures and the changes are near linear for both (Fig. 5c and d). The response to ice thickness is more complex. Thicker ice columns result in lower SDR due to thicker layers and shallower gas concentration gradients. However, ice columns larger than ∼3000 m have a greater likelihood of basal melting, potentially removing old ice. Therefore, the sensitivity in Fig. 5b should not be interpreted to suggest maximizing ice thickness will minimize SDR. We explore scenarios with basal melt in more detail in Fig. 7.

The O₂ / N₂ ratio model runs show similar results to those for CO₂. Accumulation rate's impact on gas concentration gradients dominates the impact from colder temperatures (Fig. 6a), and its relatively steep slope also shows its importance among the forcings. The O₂ / N₂ ratio SDR is mildly more sensitive to GHF, due to higher sensitivity of O₂ permeability to temperature compared to CO₂. Similarly to CO₂, minimizing surface temperature and GHF will minimize SDR for the O₂ / N₂ ratio, too (Fig. 6c and d). Unlike CO₂, ice thickness has a relatively weak effect on the O₂ / N₂ ratio SDR. In thicker ice columns, we find the impact on temperature slightly dominates the impact on gas concentration gradients as demonstrated by the slightly positive slope in Fig. 6b. This arises from a higher sensitivity to temperature in the permeability of O₂ compared to CO₂. However, in shallower ice columns, where temperatures are cooler compared to thicker ice columns, the relatively flat slope implies the impacts on temperature and layer thinning are about equal and opposite. The lower dissociation pressure of O₂ compared to CO₂ causes more diffusion in the warmer temperatures of thick ice columns. Ice thickness's weak effect on the O₂ / N₂ ratio SDR is further highlighted in Fig. 7.

Basal melt is important to consider for SDR and site selection. Under scenarios where basal melt rates are low, about 0.1 mm yr⁻¹, ice older than 1.5 Ma is removed but ice of 1.5 Ma age remains. The melting of the older ice, without removing the 1.5 Ma ice, creates additional vertical space for the 1.5 Ma ice to occupy, thus reducing the thinning. The reduced thinning of 1.5 Ma ice thus results in improving gas signal preservation. Figure 7 shows SDR values for CO₂ and the O₂ / N₂ ratio in 1.5 Ma ice under varying GHF and ice thickness, with fixed accumulation rates of 3 cm yr⁻¹ and surface temperatures of -60 °C. The signal preservation enhancing effect of low melt rates is apparent at the boundary between preserved 1.5 Ma ice and melted ice, where SDR values are lower by about 5 % (Fig. 7). This is most important for CO₂ signal preservation, as we see that the O₂ / N₂ signals are almost fully damped above 45 m W m⁻². However, producing such a low melt rate requires a specific range of forcing values in this simplified model, so a site with these conditions is likely rare.

The gas diffusion model is now applied to the COLDEX study area (Fig. 8). We will first discuss the distribution of old ice in each of the three regions – the Saddle Region, the Deep Basin, and the Foothills – then discuss the CO₂ and the O₂ / N₂ ratio SDRs. The accumulation rate and ice thickness inferred from the airborne radar data (Young et al., 2025a) is shown in Fig. 8a and b and the surface temperature forcing in Fig. 8c. Estimates of GHF (Stål et al., 2020; Shen et al., 2020; An et al., 2015; Maule et al., 2005; Martos et al., 2017; Shapiro and Ritzwoller, 2004; Purucker et al., 2013; Hazzard and Richards, 2024) show considerable variability and their relative accuracy cannot be assessed; therefore, we use uniform GHF values of 45, 50, and 55 m W m⁻². We consider the near-basal ice age as the age of ice that is 2 % of the ice column's thickness above the bed (Fig. 8g–i), which is between 40 and 80 m above the bed in the COLDEX study area. We use the 2 % threshold to facilitate comparison among the study area.

The Saddle Region and the Foothills retain old ice, while the Deep Basin has mostly lost the oldest ice to basal melt (Fig. 8g–i). Only in the low GHF scenario does the Deep Basin retain old ice. Figure 8d–f shows how each GHF scenario increases the basal melt, particularly in the Deep Basin. It is also important to note that the Saddle Region is downstream from the Deep Basin and advection is not considered in our model; we discuss the effects of advection in Sect. 4.1. The Foothills contain the oldest ice under all GHF scenarios, but the calculated age is variable due to the considerable variability in ice thickness in the region.

We discuss SDR in terms of its value at 1.5 Ma. The lowest CO₂ SDR (Fig. 8j–l) is in the Foothills and in the Deep Basin when there is old ice present. CO₂ SDR tends to be higher in the Saddle Region where accumulation rates are higher, consistent with the results in Sect. 3.2. The variable ice thickness in the Foothills contributes to variability in CO₂ SDR but is not as significant as the variability in ice age. For each GHF scenario, the CO₂ SDR varies marginally in the Foothills (∼3 %–10 %) and varies more significantly in the Saddle Region (∼18 %–30 %).

The O₂ / N₂ ratio SDR (Fig. 8m–o) follows a similar pattern to the CO₂ SDR. The lowest O₂ / N₂ ratio SDR is in the Foothills, although it is still much higher than the SDR for CO₂. Both the Deep Basin and Saddle Region have nearly 100 % SDR. In the Deep Basin, this is because of the warm temperatures in the deep ice while in the Saddle Region it is because of the high accumulation rate and steep gas concentration gradients in the basal ice. The Foothills is the only region with SDR significantly below 1, due to the effects of low melt rates as described in Sect. 3.2. Although, there is considerable variability in the SDR in the Foothills.

Uncertainties in GHF have a larger effect on the distribution of old ice compared to the diffusion of gas signals. In the Deep Basin, where ice thickness is consistently around or above 3000 m, we see the amount of old ice present changes dramatically with different GHF values. At 45 m W m⁻², old ice is abundant in the basin, only absent where ice thickness nears 4000 m. However, at 50 m W m⁻² most of the old ice is gone except towards grid-south, and at 55 m W m⁻² there is virtually no old ice in the basin. Assuming uniform GHF, the oldest ice will be located near either the South Pole, the Foothills, or both according to the model, with the Foothills having better conditions for atmospheric gas signal preservation. Additionally, advection will affect the presence of old ice in the Saddle Region, as discussed in Sect. 4.1.

We have presented 1D results and have not assessed the impact of advection. Advection will be important to consider because even the slow horizontal velocities in the region, 1–2 m yr⁻¹ in the survey region, imply that 1.5 Ma ice has travelled hundreds of kilometers. Unfortunately, modeling SDR for the full study area with flowline models is intractable both because of the computational time and the increasing number of assumptions needed to force the model. We note that the gas diffusion model can be applied to any ice thinning and temperature scenario and thus is compatible with output from ice flow models as long as this information is tracked (e.g. Chung et al., 2023; Parrenin et al., 2025). Consideration of specific ice core sites should employ flow band models where parameter ranges for the upstream area can be carefully considered.

The 1D model results are best for gaining qualitative information about the broader regions which are likely to best preserve atmospheric gas records. The primary limitation is that small scale variations in forcing parameters, such as bedrock topography, can produce results that appear favorable but where advection would have instead significantly imprinted the conditions from upstream on the ice at that location. Thus, considering the conditions in the upstream direction is useful for interpreting the results at any individual location. For example, in our results the model signifies the presence of old ice in the Saddle region (Fig. 8g–i). However, ice flows from the Foothills, through the Deep Basin, where old ice likely melts away, before reaching the Saddle Region. Thus, the Saddle Region is less likely to preserve old ice than the 1D model results may suggest.

The most favorable site conditions for the preservation of gas signals in a deep ice core are where accumulation rates, basal melt rates, and surface temperatures are low, and ice thickness is moderate, between ∼2500 and ∼3000 m. If a location with low GHF can be identified, then greater ice thicknesses are preferred because basal melt is avoided and the gas concentration gradients are smaller, reducing the amount of diffusion.

The Deep Basin, due to its large ice thickness, results in too much basal melt, removing the old ice. Even in the low GHF scenario (45 m W m⁻²), some of this region experiences basal melt (Fig. 8d). We note that if the GHF is unusually low, the Deep Basin could provide exceptional preservation conditions; however, geophysical observations supporting such a unique combination would be necessary to justify further exploration in this region. In the Saddle Region, accumulation rates are relatively high (∼6 cm yr⁻¹), steepening gas concentration gradients in the basal ice and increasing signal diffusion. The SDR is higher in the Saddle Region than in the Foothills, as seen in Fig. 9. We also note that the ice has flowed across the Deep Basin, so if melt has removed the old ice in the Deep Basin, it would not be present in the Saddle Region. Thus, both the Deep Basin and the Saddle Region are not optimal locations for a deep ice core. While there remains the possibility of finding an ice core site in these regions, it would likely require an unusually low GHF in the Deep Basin (e.g. Hazzard and Richards, 2024) so that ice is not removed there.

The lower accumulation rates and moderate ice thickness make the Foothills a more promising region for a deep ice core. Old ice is more common and SDRs are lowest in this region. Within the Foothills, the grid-south portion of the foothills have thicker ice columns than the grid-north portion, increasing melt rates and decreasing the old ice present. This leaves the grid-north foothills as the most promising location (Fig. 9). Even though this is the most promising region, the presence of 1.5 Ma ice is variable and should be evaluated at a particular site to ensure its presence. Sites where the melt rate might be low enough, but non-zero, to decrease SDR as described in Sect. 3.2 should not be sought, since the narrow range of necessary forcings, the uncertainties associated with the model, and the impact of advection make looking for such a site impractical.

Our results show that CO₂ SDR for 1.5 Ma ice does not exceed 13 % in the grid-north Foothills and averages 5 % given 50 m W m⁻² GHF (Fig. 8k). However, the SDR for the O₂ / N₂ ratio in the grid-north Foothills is still high, with a mean value of 89 % (Fig. 8l). There is uncertainty associated with the fraction of gas signal lost to diffusion in the model arising from uncertain gas parameter values (see Sect. 4.4). Nonetheless, we still expect that CO₂ signals will experience only a small amount of diffusion, while the O₂ / N₂ ratio will experience significantly more. The difference between the SDR for CO₂ and the O₂ / N₂ ratio is partly due to the different frequency in the climate record; the SDR for a 20 kyr CO₂ signal is 28 % for a typical site in the Foothills whereas the 40 kyr SDR is 8 %. Therefore, even though old ice is likely present in the grid-north Foothills and CO₂ may be well preserved, the damping of precession signals in the O₂ / N₂ ratio from this region may preclude dating of the ice core. Measurements of total air content (TAC) may provide another method for dating an old ice core (e.g. Raynaud et al., 2007), but this method comes with its own complications (Vudayagiri et al., 2025) as climate and elevation changes can overprint the insolation signal. Future work could consider how TAC signals may diffuse in old ice. For 1.2 Ma ice (when the MPT is thought to have begun; Clark et al., 2006) the SDR for the O₂ / N₂ ratio is lower than at 1.5 Ma (∼0.5–0.7 in the grid-north Foothills), so it may be possible to track precession cycles through the MPT.

The 1D model we use assumes a continuous depth-age relation to the bed; however, radar imaging shows that stratigraphic layering is lost hundreds of meters above the bed and finds diffuse scattering in portions of the deep ice (Young et al., 2025a). Work around Dome C suggests there may be basal layers of stagnant ice (Lilien et al., 2021; Chung et al., 2023; 2024), which can affect the inferred depth-age relationship. Analysis of the radar data at ice core locations (Mutter and Holschuh, 2025) show that the continuous climate record can be preserved at depths with diffuse scattering. We assume that the climate record is undisturbed to the bed in this study. However, if instead the basal unit is mechanically decoupled (e.g. Lilien et al., 2021; Chung et al., 2023), then the thickness of the deforming ice column is less than the total ice thickness. This would result in greater layer thinning as well as colder temperatures because the old ice is higher in the ice column.

To assess the impact of a potential basal ice layer, we perform three model runs and compare their SDRs. Case 1 is the control with 2700 m ice thickness, 50 m W m⁻² GHF, 2 cm yr⁻¹ accumulation rate, and -60 °C surface temperature. Case 2 investigates the impact of a change in layer thickness while keeping the temperature the same. Case 3 investigates the impact of a change in temperature while keeping the layer thickness the same.

The temperature and age profiles of the three cases are shown in Fig. 10. We do not directly incorporate a non-deforming basal layer and instead adjust the GHF to simulate its impacts. Case 2 simulates a 10 % (270 m) basal ice layer to assess the impact of layer thinning from a non-deforming basal ice layer; we model a thinner ice column (2430 m) but match the Case 1 temperature. Case 3 simulates a 3000 m ice column with the bottom 10 % (300 m) non-deforming to assess the impact of a change in ice temperature from a basal ice layer; we model the same thickness (2700 m, so the depth-age profile is the same), but match the temperature profile to a model run of Case 1 extended to 3000 m ice thickness (Case 1^* in Fig. 10) by reducing the GHF. The cases and resulting SDR are summarized in Table 3.

In Case 2, a thinner deforming ice column increases CO₂ SDR and decreases the O₂ / N₂ ratio SDR. This aligns with what we would expect given the parameter sensitivity analysis in Sect. 3.2 (see Figs. 5b and b). In Case 3, a lower ice temperature from the presence of a basal ice layer decreases the CO₂ and the O₂ / N₂ ratio SDRs. This also aligns with our expectations since the presence of a basal ice layer decreases the ice temperature, reducing diffusion. The difference in SDR for all cases is small, so we do not expect the presence of a basal ice layer to dramatically alter the preservation of gas signals. In each case, CO₂ remains well preserved and the O₂ / N₂ ratio is poorly preserved.

We perform sensitivity studies to assess the possible implications of the uncertainty in gas permeation parameters for our result. All sensitivity runs use forcing values identical to those in Fig. 3 (2 cm yr⁻¹ accumulation rate, 3000 m ice thickness, 50 m W m⁻² GHF, -60 °C surface temperature). Salamatin et al. (2001) report a ±15 % uncertainty for the permeation coefficient of O₂, so we conduct simulations using permeation coefficients that span this range. Ahn et al. (2008) do not provide an uncertainty for the permeability of CO₂ so we apply the same 15 % uncertainty range. Oyabu et al. (2021) have previously demonstrated that O₂ permeation values an order of magnitude faster than those we consider here yield unrealistically high smoothing compared to O₂ / N₂ measurements from the Dome Fuji core. Those researchers also show that the permeation coefficients of Salamatin et al. (2001) yield diffusive smoothing in reasonable agreement with the Dome Fuji measurements, increasing confidence in our parameterizations. However, the permeation values provided by Salamatin et al. (2001) (the “slow set”) are tested over a limited temperature range, and the values given by Ikeda-Fukazawa et al. (2004) (the “fast set”) approach the values in the “slow set” at higher temperatures, like those near the bed of the ice sheet. Thus, our use of the “slow set” in this study may provide a more conservative estimation of diffusive smoothing of O₂ / N₂. Future ice core measurements may improve our understanding of the temperature dependence of these permeation coefficients. Table 4 shows the SDR for each gas from each model run. Uncertainty in the permeation coefficient of CO₂ affects the SDR by <1 %. Uncertainty in the permeation coefficient of O₂ can change the O₂ / N₂ ratio SDR by about ±5 %. The study area will be affected by this uncertainty equally, and so the pattern of where SDR is low will not be altered significantly by these results. The expected SDR we find in this study is much more dependent on ice sheet physical properties than the uncertainty in gas permeation.