On the gas-ice depth di ff erence ( ∆ depth ) along the EPICA Dome C ice core

Introduction Conclusions References


Introduction
Ice cores provide a wealth of information on past climatic variations (Jouzel et al., 2007;Pol et al., 2010) and on past greenhouse gases concentrations (L üthi et al., Introduction Conclusions References Tables Figures
To interpret the records from ice cores, it is essential to derive accurate chronologies (e.g.Parrenin et al., 2007b).One of the peculiarities of ice core dating is that two age scales need to be derived: one for the ice matrix and one for the gas phase.Gas bubbles are always younger than the surrounding ice because they close off and trap the air at 50-120 m (depending on site conditions) below the surface, after the snow has densified into ice (Schwander and Stauffer, 1984).What is important for paleoclimatic studies is the Lock-In Depth (LID), where gas diffusion becomes negligible, which is slightly smaller than the Close Off Depth (COD), where it is not possible to pump air (Witrant et al., 2011).The determination of this ice/gas offset is essential to derive the phase relationship between proxies recorded in the ice phase and in the gas bubbles.As an example, CO 2 was estimated to lag Antarctic temperature changes by 800 ± 600 yr during the last deglaciation (Monnin et al., 2001), by 800 ± 200 yr during termination III (Caillon et al., 2003) and on average by 600 ± 400 yr during the last three deglaciations (Fischer et al., 1999).This finding suggests that CO 2 was an amplifier rather than the initial trigger of glacial terminations.
The gas/ice offset can be characterized in two different ways.∆age measures the difference in age between the ice and gas phases at any given depth.∆depth, on the other hand, represents the depth difference between gas and ice of the same age.
Each parameter has advantages and drawbacks.∆age is fixed when the gas is locked in and does not evolve with time because there is no relative movement of the gas bubbles or hydrates with respect to the surrounding ice.∆age is, however, strongly dependent on the rate of surface snow accumulation at the site, which is poorly constrained for the past: for a given LID and density profile, ∆age is inversely proportional to the accumulation rate.By contrast, ∆depth is independent of the reference age scale used.However, it continually evolves as the ice thins, which complicates its evaluation.Inversely, having observations of ∆depth from ice and gas proxies can provide useful information on the past flow of ice.In this paper we will focus on the evaluation of the ∆depth along the EDC ice core.There are several ways of estimating it and these fall into two categories: (1) estimation of the initial LID of gas bubbles and estimation of the thinning of snow/ice layers; (2) determination of synchronous events in gas and ice proxy records.In this study, we will apply different approaches to deduce ∆depth estimates along the EDC ice core.These various estimates will be inter-compared and discussed.
Note that in the following, we have to deal with datasets on both the EDC96 and EDC99 ice cores.We systematically transfer all EDC96 datasets to EDC99 depths using a linear interpolation of the volcanic tie points between both cores (Parrenin et al., 2012).We use the same depth-depth relationship for both gas and ice datasets, i.e. we assume that ∆age as a function of age is the same for both cores.

Methods
∆depth from ice flow and densification models From a mechanical point of view, ∆depth is given by: where D(z ) and τ(z ) are respectively the density of the material relative to pure ice and the thinning as a function (the ratio of a layer thickness to its initial thickness) of the depth z and h is the Lock-In Depth (LID) at the time t when the initial snow layer, which is now ice at depth z − ∆depth(z), was at surface.We further define h ie the Lock-In Depth in Ice Equivalent (LIDIE): Introduction

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Full in the firn and because of the gradual bubble close off process, any depth contains a distribution of age which can be accurately approximated by a log-normal function (K öhler, 2010).We implicitly use here the median of this log-normal distribution as the so-called gas age for any given depth.D(z',t = 0) can be estimated by measuring the weight and the volume of the ice cores.However, no reliable quantitative proxy has been proposed for τ(z , t) and D(z , t) and their evaluation usually relies on ice flow (e.g.Reeh, 1989;Parrenin et al., 2007a;Salamatin et al., 2009b) and firn densification modelling (e.g.Herron and Langway, 1980;Arnaud et al., 2000;Salamatin et al., 2009a).We will detail in the following the ice flow model and firn densification model used in this study.

Ice flow model
A one-dimensional (1-D) ice flow model has been used to construct the modelled age scale X m at the EDC drilling site and to derive a modelled thinning function τ m (Parrenin et al., 2007a).In this model, the vertical velocity u z of the ice relative to the bedrock is expressed as: where z is the vertical coordinate of the ice particle (oriented toward the top), z = z−B is the distance to the bedrock (B is the bedrock elevation), ζ = z/H is the non-dimensional vertical coordinate, m is the melting rate at the base of the ice sheet, a is the surface accumulation rate, H is the ice thickness and ∂H ∂t is its temporal variation.ω (ζ ), called the flux shape function (Parrenin et al., 2007c), depends on the non-dimensional vertical coordinate and is the contribution of one sliding term and one deformation term: where s is the sliding ratio (Ratio of the basal horizontal velocity to the vertically averaged horizontal velocity; it is 0 for no sliding and 1 for full sliding) and ω D (ζ ) can be approximated by [Lliboutry, 1979]: where p is a parameter for the vertical profile of deformation ω D (ζ ).The values of p, m and s are assumed constant through time.
The past variations of ice thickness H(t) are obtained from a 1-D model (Parrenin et al., 2007a) fitted onto the results of a 3-D model of the Antarctic ice sheet (Ritz et al., 2001).The main process is the reduced accumulation rate during glacial times, which induces a lower elevation (and reduced ice thickness) at Dome C during glacial periods.However, preliminary results with an improved 3-D model with increased spatial resolution suggests that the presence of an ice sheet in the Ross embayment might limit the impact of a reduced accumulation on the elevation at the EDC site, at least during the last glacial maximum (Ritz, personal communication, 2012).This is why, in the following, we will also test the hypothesis of zero ice thickness variations at the EDC site.This appears as an extreme case, given that some geomorphological data in the Transantarctic Mountains show little elevation change of the Antarctic plateau for the last glacial maximum (Denton et al., 1989), despite the presence of the ice sheet in the Ross embayment.
Accumulation A m and temperature T are deduced from the deuterium content of the ice extracted from the drill core, through the following relationships:

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Full where A 0 and T 0 are surface accumulation and temperature for a reference deuterium content of −396.5 ‰ (roughly corresponding to the present-day value).∆δD smo is a 50-yr smoothed version of ∆δD cor because the accumulation rate A m is supposed to be related to the isotope content of the deposited snow only over a certain time interval (high frequency variations of deuterium may be affected by post depositional processes such as wind scouring).The poorly constrained glaciological parameters p = 2.30, m = 0.066 cm-of-ice yr −1 , s = 2.23 %, A 0 = 2.841 cm-of-ice yr −1 and β = 0.0157 were obtained by fitting independent age markers identified within the core (Parrenin et al., 2007a).The inferred value for β appears consistent with modern spatial gradients in central East Antarctica (Masson-Delmotte et al., 2008).Given the inability of the model to fit some age markers (Dreyfus et al., 2007;Parrenin et al., 2007b), the thinning function τ and surface accumulation rate A were tuned a posteriori using a spline method so that the age scale fit these age markers (see appendices of Parrenin et al., 2007b;Dreyfus et al., 2007).
It is difficult to quantify the uncertainty on the modeled thinning function τ m (z) because we do not know which processes are missing in the ice flow models.Here we consider only the non-laminar ice flow effects and assume that the error they induce on ln(τ m ) is: where D(z) is the density of the material relative to pure ice and k is a proportionality coefficient.We infer the value of k with a residual approach using the multiplicative correction for the thinning function C(z) which has been inferred from the orbital tuning of δ 18 O atm in the 2700-3200 m interval of the EDC ice core (Dreyfus et al., 2007).k is simply given by the standard deviation of the following function f (z) : which is represented in Fig. 1.This gives k = 0.0974 and the resulting σ ln(τ) function is plotted in Fig. 7.

Firn densification model
For the firn densification modeling exercise and the determination of ρ (y), we used the Arnaud/Goujon model (Goujon et al., 2003).Arnaud et al. (2000) developed an advanced densification model which considers two densification stages: pure sliding of snow grains for density lower than ∼0.55 g cm −3 , and pure deformation of grains for density higher than ∼0.55 g m −3 .Goujon et al. (2003) then incorporated heat transfer into this model.In the applications below we used a surface density of 0.35 g cm −3 .The Lock-In density ρ(y = h) is determined from the Total Air Content (TAC) of the ice (Martinerie et al., 1992(Martinerie et al., , 1994;;Raynaud et al., 2007) corrected for local atmospheric pressure changes (due in particular to elevation changes) using the perfect gas law.
In the applications below, for simplification and based on the approach by Martinerie et al. (1992Martinerie et al. ( , 1994)), we use a conventional linear empirical relationship between the volume of pores at Close Off (V c , cm 3 g −1 ) and surface temperature T S (K) as: The evolution of closed porosity in the firn, P closed , is deduced from the following relationship: which has been calibrated with P closed and P total measurements on several ice cores from Greenland and Antarctica (Jean-Marc Barnola, personal communication, 2009).This relationship means that at Close-Off, 37 % of the pores are closed.The LID is further defined, at EDC, when 20 % of the pores are closed.Introduction

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Full The steady LID, ∆age and LIDIE/LID ratio simulated by the Goujon/Arnaud model are represented in Fig. 3 in a surface temperature-surface accumulation diagram for a surface density of 0.35 g cm −3 .Qualitatively speaking, LID is greater for a greater accumulation or for a lower temperature, while ∆age is greater for a lower accumulation or for a lower temperature.The LIDIE/LID ratio is practically constant: it only varies between 0.682 and 0.702.∆depth from ice flow modelling and δ 15 N-based estimates of firn thickness The ice flow modelling part of this estimate has been described above.We use here the variations of ice thickness at EDC as derived for the EDC3 age scale (Parrenin et al., 2007a, b).Now h is estimated using the fact that, below a convective zone of height h conv where the air is mixed (Colbeck, 1989(Colbeck, , 1997)), gravitational settling enriches heavy isotopes of inert gases (such as δ 15 N of N 2 and δ 40 Ar) proportionally to the diffusive column height h diff (Craig et al., 1988;Sowers, 1989;Dreyfus et al., 2010) until gases no longer diffuse in the open pores .We implicitly assume here that all gases stop diffusing at the same depth.Note that a recent study suggested that some trace gases continue to diffusive below the LID defined by the start of the δ 15 N plateau (Buizert et al., 2011).In delta notation, this gravitational fractionation is expressed as: where ∆m is the mass difference between species (kg mol −1 ), g is the gravitational acceleration (9.81 m s −2 ), R is the universal gas constant (8.314J mol −1 K −1 ) and T is the firn temperature (K).Equation ( 12) can be approximated within 0.02 % with: Thermal fractionation of δ 15 N occurs because of the temperature difference ∆T between the surface and the LID: where G is the vertical temperature gradient in the firn.Ω(T ) has been estimated from laboratory measurements (Grachev and Severinghaus, 2003).
Conversely one can deduce h from the δ 15 N data (Dreyfus et al., 2010): In the applications below, we will assume that there was no convective zone at EDC during the last 800 kyr, in agreement with current observations (Landais et al., 2006).One of the reasons for variations in the convective height is the change of wind stress.
GCM experiments for the LGM show little variations in wind on the East Antarctic plateau (Krinner et al., 2000).Note that we have evidence of a large convective zone at some sites and for the present (Bender et al., 2006;Severinghaus et al., 2010).
We further assume a constant 0.008 • m −1 vertical temperature gradient in the firn, as measured for the present between 20 and 100 m (L.Arnaud, personal communication, 2012).We take the surface temperature as computed for the EDC3 age scale (Parrenin et al., 2007a), as a function of the ice depth.We also need a prior ∆depth estimate to convert the ice depths to gas depths and we use the EDC3 scenario 1 estimate (Loulergue et al., 2007).We estimate the uncertainty on the temperature estimate to be <4 K which translates into a <2 % 2σ error on h.We estimate the uncertainty on the temperature gradient to be <0.003which translates into a <1 % 2σ error on h.Following the Goujon/Arnaud model simulations (see Fig. 3c), Eq. ( 2) is simplified into:

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Full  (2) would imply a varying difference between LID and COD.In total, we estimate the 2σ error of Eq. ( 16) to be 5 %.Equation ( 1) is solved assuming the thinning function expressed as a function of z ie , the ice equivalent depth, was the same at the time of deposition as for the present.The error of this approximation is due to the varying basal melting/accumulation ratio and to the varying ice thickness (Parrenin et al., 2007a) but we evaluate it to be <0.1 % on ∆depth.The δ 15 N record from the EDC ice core covers the last three glacial terminations and five glacial-interglacial cycles between 300 and 800 ka (Dreyfus et al., 2010).

∆depth from ice and gas synchronisation to GRIP
∆depth at the depth of the 10 Be peak (Raisbeck et al., 2007) in the EDC ice core can be estimated by linking the ice and gas signals to GRIP (Loulergue et al., 2007).
The ice link is obtained by 10 Be synchronisation of EDC and GRIP for two 10 Be subpeaks during the Laschamp event (Raisbeck et al., 2007).The gas link is obtained by matching the EDC CH 4 record to the GRIP ice isotopic record (Fig. 4), assuming that these two records are synchronous during the rapid DO transitions (Fl ückiger et al., 2004;Huber et al., 2006).On Fig. 4, we align the onsets of DO9 and DO11 and 1099 Introduction

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Full remark that the onset of DO10 is also aligned.Linear interpolations allow to obtain the corresponding gas depths in EDC99.Note that our horizontal scale is expressed in GRIP ages, since there are significant variations of accumulation which would make the interpolation inaccurate in depths.It is not necessary to use an age scale for EDC since the variations of accumulation are small and the variations of thinning is <2 % in the considered interval.This finally gives these two estimates of the ∆depth at EDC99: ∆depth at 782.9 m = 48.9± 2 m (2σ); ∆depth at 791.5 m = 48.2± 2 m (2σ).The uncertainty accounts for the uncertainty in the 10 Be sub-peaks positions in EDC (1.1 m) and in GRIP (1.1 m EDC equivalent depth) and for the GRIP-EDC synchronization (1.3 m).

∆depth from ice and gas synchronisation to EDML
Another approach to deduce EDC ∆depth is to synchronize the ice core records, both in the ice and gas phases, to a higher accumulation Antarctic ice core, such as EDML (see Fig. 5) which has a better constrained ice/gas offset (Loulergue et al., 2007).Such an approach has already been applied to constrain the Vostok gas/ice offset using data from the Byrd ice core record (Blunier et al., 2004;Bender et al., 2006) and the EDC gas/ice offset using EDML (Loulergue et al., 2007).The EDC and EDML ice cores have been synchronised (Severi et al., 2007;Ruth et al., 2007) using volcanic stratigraphic markers recorded in the ice phase.Here we also derive 20 new CH 4 tie points (see Table 1 and Fig. 6) [Loulergue et al., 2007[Loulergue et al., , 2008;;Schilt et al., 2010] mainly at the onsets of Greenland Interstadials (GI) over the period 0-140 kyr BP.Note that we did not use systematically the tie points of Loulergue et al. (2007) or of Schilt et al. (2010) since, (1) we do not use ends of GIs because they are less well marked than the onsets and therefore bring little information with respect to the neighboring onsets, (2) we do not use GI2 and GI9 because we reckon their identification is too ambiguous (3) we choose the tie points exactly at the mid-transitions.The evaluation of ∆depth at EDC now relies on its evaluation at EDML.We derived the later from Eq. (1).For the thinning, we did not use estimates based on an ice flow model (Huybrecht et al., 2007) 1100 Introduction

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Full because for the same age, the depth is larger at EDML than at EDC and the evaluation of the thinning function from ice flow modelling thus becomes inaccurate.Instead, we fixed the EDML1 age scale (synchronized to EDC3, Ruth et al., 2007), used EDML accumulation rates from Loulergue et al. (2007, scenario 1) and deduced an EDML thinning function.For the LID, we used the Goujon et al. (2003) densification model forced with the temperature and accumulation estimates as derived from Loulergue et al. (2007, scenario 1).The LID is taken at 5 % of closed porosity.This method is more precise than a direct evaluation of the ∆depth at EDC from modelling.Indeed, the accumulation rate is 3 times higher at EDML than at EDC.An error in EDML LID thus has a 3 times lower impact than at EDC in terms of ages.
There are 4 sources of uncertainty in this EDML-synchro based approach: (1) the uncertainty in the gas (CH 4 ) synchronisation, (2) the uncertainty in the LID estimate at EDML, (3) the uncertainty in the thinning function at EDML and (4) the uncertainty in the ice (volcanic) synchronisation (including the interpolation between two neighboring volcanic tie points).We estimate uncertainty (1) (2σ) as half the duration of the CH 4 transition.Uncertainty (2) (2σ) is thought to be <20 % at EDML (Landais et al., 2006) i.e. <7 % at EDC.Based on the relative duration of events in different glaciological time scales (Parrenin et al., 2007b) we deduce that uncertainty (3) (2σ) is <10 % (Parrenin et al., 2007b).With the same argument, uncertainty (4) (2σ) is estimated to be <10 % of the distance to the nearest tie point, i.e. we neglected the uncertainty in the tie points.
In order to compute the total uncertainty, we assume uncertainties 1, 2, 3 and 4 to be independent to compute the total uncertainty.
Note that a recent study (K öhler, 2010) suggested that aligning the mid-transitions of CH 4 in different ice cores induces an error because of the different diffusion times of the gas signals.We think their conclusion only applies if one defines the gas age as the minimum gas age of the distribution.We defined here the gas age as the median of the distribution and we are therefore free from such an error.Introduction

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Full

∆depth from ice and gas synchronisation to TALDICE
The method is the same as in the previous sub-section (see Fig. 5).Its advantage is also based on the fact that TALDICE accumulation rate is 3 times higher than EDC accumulation rate.The EDC and TALDICE ice cores can be synchronized in the ice phase using volcanic markers for the last 42 kyr (Severi et al., 2012) and isotopic records elsewhere (Jouzel et al., 2007;Stenni et al., 2011, see Table 2) and in the gas phase using CH 4 records (Loulergue et al., 2008;Buiron et al., 2011, see Table 3 and Fig. 6).Note that we do not use the tie points of Buiron et al. (2011) since they are not always placed exactly at mid-transitions.We also restricted the tie point selection to the part of CH 4 records bearing the less disputable common structure.We use ∆age at TALDICE as computed by Buiron et al. (2011).
The uncertainty is calculated in the very same way as for the synchronisation to EDML.

∆Depth from the thermal bipolar seesaw hypothesis
Following the so-called thermal bipolar seesaw hypothesis (Stocker and Johnsen, 2003), Greenland temperature is related to the derivative of the Antarctic temperature derived from EDC isotopic record (Barker et al., 2011).The most viable mechanism for abrupt climate changes in the North Atlantic region involves reorganizations of the ocean circulation (Stommel, 1961;Ruddiman and McIntyre, 1981) but atmospheric mechanisms may also be at play in the antiphase relationship proven for the last glacial period (Blunier et al., 1998;Blunier and Brook, 2001;EPICA community members, 2006;Capron et al., 2010).Using the seesaw hypothesis, we can consequently synchronise the deuterium content of the EDC ice (a proxy for Antarctic temperature) with the CH 4 content of the EDC (Loulergue et al., 2008) gas bubbles (a proxy of Greenland temperature) and produce ∆depth estimates during periods of fast CH 4 variations corresponding to maximas or minimas in the deuterium record.

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Full To localize the maximas or minimas in the deuterium record, we used the synthetic Greenland temperature curve GL T syn from Barker et al. (2011) calculated from the deuterium record of ice at EDC.This curve was constructed by a mathematical process which involves separation of the high and low frequency components of the Antarctic temperature record and differentiation of the high frequency component before it is recombined with the low frequency component.Identifying an extrema in the EDC deuterium record thus corresponds to identifying a fast transition in the GL T syn curve.The fact Barker et al. (2011) were able to reconstruct a curve from an Antarctic ice isotope record which resembles the Greenland ice isotope record and in particular exhibits similar fast transitions is another proof that the seesaw was at play during the past.
In Fig. 7, we compare the GL T syn curve of Barker et al. (2011) and the EDC deuterium record of Jouzel et al. (2007) with the CH 4 record from EDC (Loulergue et al., 2008) on a depth scale.Using these constraints, 82 tie points (see Table 4) are derived between the two records, mainly at times of fast variations in Greenland temperature.
These tie points correspond to maxima and minima in the EDC deuterium record (see Fig. 7).∆depth estimates are simply computed as the depth of the transition in the methane record minus the depth of the transition in the GL T syn curve (or equivalently to the depth of the maxima or minima in the deuterium record).
There are two sources of error in this procedure.First, the identified transitions in GL T syn and CH 4 may not correspond to the same event.We therefore tagged the pairs of tie points as "virtually certain" or "tentative".Second, even if the transitions in GL T syn and CH 4 correspond to the same event, there is an error linked to the determination of the depth of the transitions in both curves.To evaluate this (2σ) error of these ∆depth estimates, we added the error of the depth estimates of the transition in the methane and GL T syn curves respectively.These errors are evaluated as half of the duration of the transition.
The reasons why we used GL T syn and not the raw deuterium record are: (1) it is easier and more accurate to select a mid-transition than an extrema and (2) it is

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Full also easier to estimate the error in the tie point picking as half of the duration of the transition.

Discussion
In Fig. 8, we compare the various ∆depth estimates derived previously.Several conclusions can be outlined.

Confirmation of the bipolar seesaw anthiphase
The GRIP-synchro based estimate of ∆depth during the Laschamp is the most accurate (±2 m) and robust (it does not rely on controversial hypotheses) estimate available among the EDC ice core data.It is important to note that this estimate is fully compatible with the bipolar seesaw-based estimate.In other words, the seesaw phasing is observed during the Laschamp geomagnetic excursion between EDC and GRIP, as was already concluded by Raisbeck et al. (2007).
A second noteworthy remark is that the EDML ice core records mainly confirm the seesaw hypothesis, as was already concluded (EPICA community members, 2006;Capron et al., 2010).One can however remark that the EDML synchro estimates tend to underestimate ∆depth during the last glacial period with respect to the seesawbased estimates, by ∼2-3 m in average, probably resulting from an underestimation of ∆depth at EDML, because a systematic offset in the CH 4 and volcanic synchronisations is unlikely.An underestimated LID by the densification model is also unlikely, because δ 15 N data shows the contrary (Landais et al., 2006).It thus leaves us only with an underestimation of EDML thinning, which may be due to an overestimation of EDML accumulation rates during the glacial.We indeed did not take into account the fact that accumulation rates are lower upstream of the EDML site, from where the ice originates (Huybrecht et al., 2007).

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Full A third remark, coming from the present study, is that the TALDICE ice core records confirm the seesaw hypothesis.Contrary to the EDML ice core, we did not observe for the TALDICE ice core a systematic offset with respect to the seesaw-based estimates.
In the detail, there are EDML-based or TALDICE-based estimates which deviate significantly from the seesaw-based estimates.Note that we used exactly the same depths for the CH 4 transitions in all three methods.At ∼651.90 m (onset of DO4), the seesawbased estimate is very small (44.64 m) compared to the EDML-based and TALDICEbased estimates.The corresponding maxima in the deuterium curve is ambiguous and it is why this tie point has been tagged as "tentative".Another possible explanation is that EDC3 underestimates the duration of events in this interval, leading to overestimated thinning function at EDML and TALDICE.At 809.2 m (onset DO11) and 848.5 m (onset DO12), the TALDICE-based estimates are very small (53.23 m and 48.42 m) compared to the EDML-based and seesaw-based estimates.We note however that we are here beyond the EDC-TALDICE volcanic synchronization, so this discrepancy can comes from a poor EDC-TALDICE ice synchronization.At 1105m, 1142m, 1239m, 1431.5 m and 1473 m (onsets DO19, 20, 21, 23 and 24), the seesaw-based estimates are systematically higher than the EDML-based and TALDICE-based estimates.One possible explanation is that EDML and TALDICE ∆depths are underestimated due to an overestimation of durations in EDC3.

The glacial ∆depth paradox at EDC
Focusing now on the modelling estimates of ∆depth during the last glacial period (the last deglaciation and the last glacial period), they are on average ∼15 % larger than the seesaw-based estimates or the EDML-synchro and TALDICE-synchro based estimates.It is very likely that the modeled ∆depth may be inaccurate during this time period.We call this model-data discrepancy the "glacial ∆depth paradox at EDC".This may be due either to an overestimation of the thinning function or to an overestimation of the LID.Introduction

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Full One factor influencing the thinning function is the non-laminar flow effects.However, the amplitude of the ∆depth paradox is greater than the uncertainty on the thinning function due to non-laminar flow effects (Fig. 2).
Another factor which has a significant impact on the thinning function in the upper part of the ice sheet is the past variations of ice thickness.As previously explained, apart from the EDC3 scenario of past ice thickness variations, we tested a scenario without ice thickness variations as an extreme case (see Fig. 8).This scenario only partially solves the glacial ∆depth paradox at EDC.
The last factor that has a significant impact on the thinning function in the shallow part is the ice thickness at the site of snow deposition.The glacial ∆depth paradox at EDC could be solved if one assumes that the ice flow was not vertical in the past and that the ice originates from a site with greater ice thickness.This hypothesis is difficult to test from a modelling point of view because there are many unknown parameters in 3-D ice flow models of the Antarctic ice sheet influencing the position of the ridges and of the domes.We however remark here that the glacial ∆depth paradox at EDC only concerns the glacial part and is not present (and is even inverted) for the Eemian ice.This paradox therefore seems to have a climatic origin.Our conclusion is thus that, for reasons which are beyond the scope of the present manuscript, the firn densification model overestimates the glacial LID at EDC.A possible explanation is the effect of impurities on the densification process (H örhold et al., 2012).This remark is in contradiction with the conclusions of Caillon et al. (2003), who stated that the firn densification model applied for the termination III at Vostok correctly estimate ∆age.However, Caillon et al. (2003) based their conclusions on the assumption that δ 40 Ar is a gas phase temperature proxy, which has never been demonstrated.

The Termination II ∆depth paradox at EDC
During termination II, we have two different estimates of the ∆depth (see Fig. 8a, depth interval 1700-1800 m).On one hand the model-based estimate suggests a relatively low ∆depth.On the other hand, the seesaw method roughly agrees with the EDMLsynchro and TALDICE-synchro methods and suggests a relatively high ∆depth (we should note however that the two seesaw points are only tentative at this stage).We call this discrepancy the "termination II ∆depth paradox at EDC".There are two possible explanations for this discrepancy.Either the seesaw phenomenon is not at work during the penultimate deglaciation, as it is the case during the last glacial period and the EDML-synchro and TALDICE-synchro methods are not precise during this time period; or the modelled estimates are too low.
One possibility to reconcile the model with the seesaw based estimates would be to increase the thinning function, which would have the side effect to decrease the duration of the penultimate interglacial in EDC and to give a better agreement with the duration of this stage in the Dome Fuji ice core (Parrenin et al., 2007b).Another possibility would be to increase the LIDIE, for example by assuming that the surface temperature has been underestimated during this time period.It is indeed not clear that the δD-T relationships used in this study are valid for this time period which was warmer than the present (Sime et al., 2009).

Using ∆depth estimates in the deepest part to improve the EDC age scale
For the depth interval 2000-2800 m, ∆depth estimates regularly decrease from ∼16 m to ∼5 m.In this depth interval, the agreement between the seesaw-based and modelbased based estimates is surprisingly good.The fact that the model does not systematically overestimate the ∆depth in this depth interval, contrary to the last glacial period, may be just a coincidence: an overestimated LIDIE may be exactly compensated by an underestimated thinning function.Introduction

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Full For the depth interval 2800-3200 m, the agreement is also good.In particular, the seesaw-based ∆depth estimates reproduce well the bumps in thinning function which have been suggested based on the comparison between 18 O atm measurements and insolation variations and based on the phasing between δD and CO 2 (Dreyfus et al., 2007).We thus independently confirm the hypothesis that the flow in the bottom part of the EDC ice core is complex.
In conclusion, we thus suggest that using these seesaw-based estimates associated with new O 2 /N 2 measurements could improve the reconstruction of the thinning function and thus the evaluation of the EDC chronology in the deep part.

Validity of the δ 15 N firn thickness estimate for the last deglaciation
The δ 15 N record in association with the thinning model gives an evaluation of the ∆depth decreasing from 67 m to 45 m in the course of the last deglaciation.In this upper part of the EDC ice core, the uncertainty in the thinning function is thought to be small (Fig. 2).These ∆depth estimates are in good agreement with the estimates based on the synchronisation to EDML and TALDICE or based on the seesaw hypothesis.Consequently, we conclude that the model-δ 15 N data mismatch observed at EDC during the last deglaciation (Dreyfus et al., 2010) probably results from an incorrect representation of the densification process in firn models, and not to a varying convective height or to poorly known δ 15 N fractionation processes (Dreyfus et al., 2010).
This conclusion seems in contradiction with a study on the Vostok ice core using ice and gas synchronisation to Byrd (Bender et al., 2006) which concluded that δ 15 N underestimates the LID during the last glacial period.However, concerning this study,

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Full we note that: (1) there is no estimate of uncertainty in the Byrd-synchro method; (2) the thinning function reconstruction is a lot more uncertain than in our case because the coring point at Vostok is not situated on a dome (Parrenin et al., 2004); (3) the ice synchronisation is less precise than in our study because it is based on the ice isotope data; (4) the gas synchronisation is also less precise because it is based on a smaller number of CH 4 measurements.
In consequence, the δ 15 N data seems to be a more appropriate tool as compared to the current densification models to estimate the LID during the last deglaciation at EDC.Is this conclusion valid for other time periods and for other Antarctic sites where a model -δ 15 N data mismatch has been observed, such as Vostok (Sowers et al., 1992;Caillon et al., 2003), EDML (Landais et al., 2006), Law Dome (Landais et al., 2006) andDome Fuji (Severinghaus et al., 2010, based on the data by Kawamura, 2000)?Future studies similar to the one developed in this article are needed to answer this question.

Conclusions
We have shown that the bipolar seesaw antiphase relationship is generally supported by the ice-gas cross synchronisation of EDC to the GRIP, EDML and TALDICE ice cores.The glaciological model overestimates the glacial ∆depth at EDC (we called this the "glacial ∆depth paradox at EDC") and this is probably due to an overestimation of the glacial Close Off Depth by the firn densification model.The glaciological models seem to underestimate the ∆depth during termination II (we called this the "termination II ∆depth paradox at EDC").We have shown that the bipolar seesaw hypothesis confirms that the ice flow is complex in the deep part of the EDC ice core and can help improving the EDC age scale.For the last deglaciation, using δ 15 N data in association with an ice flow model gives ∆depth estimates in agreement with the estimates based on the synchronisation to TALDICE and EDML or based on the seesaw method.
Complete, precise and highly resolved δ 15 N and CH 4 records will be necessary to further improve the EDC gas and ice age scales.An automatic method to synchronize records would both bring rigor and shorten the time to accomplish this difficult task.Further studies will be needed to make the firn densification models more useful for paleoclimatic studies in Antarctic ice core records.Both the firn modeling and δ 15 N approaches need a precise evaluation of the past surface and lock-in densities and further studies are needed to better constrain them. 10Be measurements are in progress and should allow to extend the Antarctic-Greenland ice synchronisation and thus produce more ∆depth estimates based on this hypothesis-free approach.Studies on the ∆depth comparable to the present one could be applied to other low accumulation Antarctic ice cores such as Vostok and Dome Fuji.This study on the gas/ice depth offset at EDC has important implications on the phasing between CO 2 and Antarctic temperature during climatic changes and consequently on the role of CO 2 during these climatic changes.

CPD Introduction
Full    Full        [Barker et al., 2011], the EDC CH4 record [Loulergue et al., 2008] and the EDC δD record [Jouzel et al., 2007] Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | If, as proposed by H örhold et al. (2012), the densification velocity (and thus the gravitational fractionation) is influenced by impurities, δ 40 Ar should be better correlated with the impurity record than with the ice isotopic record when both are not in phase (R öthlisberger et al., 2008).Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Figure 2 :
Figure 2: Evolution of the error in the thinning function as a function of the depth in the EDC ice core.

Fig. 2 .Figure 3 :Figure 3 :
Fig. 2. Evolution of the error in the thinning function as a function of the depth in the EDC ice core.

Fig. 5 .Figure 7 :
Fig. 5. Scheme illustrating the deduction of the ∆depth at EDC from ice (volcanic) and gas (CH 4 ) synchronisation to the EDML or TADLICE ice cores and evaluation of ∆depth at EDML or TALDICE.
: A) in the depth interval 0-2000 m, B) in the depth interval 2000-2800 m, C) in the depth interval 2800-3200 m.The deuterium record has been resampled on 100 yr intervals.
(Courville et al., 2007) used a similar approximation.It corresponds to assuming that the average density of the firn is correctly predicted by the Goujon/Arnaud model.If this model would not predict the right average densification velocity but would predict the right densification profile shape, this approximation would still be valid.So this leaves us with mainly two reasons why this approximation would not be valid: (1) a variable surface density and/or (2) a variable Lock In density.Option (1) cannot be ruled out since depending on the characteristics of the surface (glazed surface, megadunes, etc.) surface densities >0.4 g cm −3 are observed on the East Antarctic plateau(Courville et al., 2007).Note that because the densification velocity is greater at surface than in depth, an error of x on the surface density has a relatively low impact of ∼ x/3 on the average density.Because the density at the COD does not change very much with time (it is well constrained by the measured Total Air Content of the ice), option

Table 1 .
CH 4 synchronisation tie points between EDC and EDML and corresponding ∆depth estimates at EDC.

Table 2 .
Isotopic synchronization tie points between the TALDICE and EDC99 ice cores.