The melt–refreeze data of 2010, 2011 and 2012, in total 1339 data points, were measured as a by-product of CH4 and N2O concentration measurements. To extract the air from the ice samples, the samples are melted in an evacuated vessel. We then refreeze the meltwater slowly from below to expel dissolved gases (see, e.g., ). The extracted gas is then expanded into the sampling loop, V2 (Fig. ). In the apparatus the mole number of extracted gas n is split between two different volumes, V1 and V2, and therefore using the ideal gas law and the gas constant R, we define TAC=V0m=n⋅R⋅T0m⋅p0=R⋅T0m⋅p0⋅(n1+n2). In the sample extraction device, we consider three volumes (Fig. 1), the head space over the ice sample Vh, the tube volume Vt and the expansion volume V2. We combine Vh and Vt to V1=Vh+Vt. The mole fractions n1 and n2 in Eq. () refer to the volumes V1 and V2, respectively. Vh is dependent on the size of each individual vessel and on the volume of refrozen meltwater in the vessel, so V1 is corrected for the small vessel-specific differences and assuming an ice density of ρice=917 kg m-3. The temperature in the headspace Vh and Vt is not homogeneous, since Vh is cooled below the freezing point, while the tubing Vt is exposed to ambient, stabilized lab temperature. T1 is therefore close to the freezing point but could not be measured directly. Instead it is determined to be 275.15 K on average through a calibration with NEEM ice and LGGE data, as described in the supplementary information of . The temperature T2 in the sampling loop is held constant at -60 ± 0.5 ∘C. The expanded gas stabilizes in the volume V1+V2 at the expansion pressure pexp, measured with the pressure gauge denoted P in Fig. . With pexp=n1⋅R⋅T1V1=n2⋅R⋅T2V2. Substituting this in Eq. () we get TAC=T0⋅pexpm⋅p0⋅V1T1+V2T2. Note that the parameter T1 may slightly vary with lab temperature and also with different extraction vessels. Assuming errors of 0.5 ∘C for T1 and T2, 0.2 mL for V1 and V2, 0.01 g for the mass m of the ice sample , and 50 Pa for pexp (at an average pexp of 4000 Pa for a sample), the resulting uncertainty in TAC is 1.3 mL kg-1, which corresponds to about 1.5 % of the TAC value in NGRIP ice.

The error used for the 2010, 2011 and 2012 data in the plots and for the interpretation was also determined by reproducibility measurements. Five adjacent samples were measured at 15 depth levels. At each of the 15 depths, we measured TAC randomly distributed over the different extraction vessels and duration of the measurement series. The pooled standard deviation of the residuals of the 75 samples is 2.2 ± 0.8 mL kg-1 (about 2.5 % of the TAC value in NGRIP ice), which is higher than the calculated analytical error of 1.3 mL kg-1. This is expected due to natural variations of TAC in the ice along the 25 cm of ice core used for the reproducibility measurements (see also Sect.  below) and variations in the number and size of the air bubbles opened on the sides of the ice cube during cutting. In order to minimize the latter effect, we cut all samples the same way, in pieces of ∼ 40 g.

The whole TAC dataset has a mean value of 93.4 mL kg-1 with a standard deviation of 4.5 mL kg-1. The measured TAC data show notable high-frequency variability which is much larger than the derived analytical error of 1.3 mL kg-1 (see Fig. ). We infer that a considerable part of the scattering in neighboring samples seems to result from the small-scale variability of the TAC signal in the ice itself. One option to verify this is to check whether the scattering diminishes with depth and therefore decreasing annual layer thickness, as described in . If the scattering is a signal in the ice itself, the standard deviation of the values in the five adjacent reproducibility samples should get smaller with increasing depth, since high-frequency variations will be smoothed by the increasing time interval per sample due to layer thinning with depth. In Fig.  the standard deviation over the reproducibility measurements is plotted vs. depth. There is a clear trend to lower scattering with depth (although not with a high correlation coefficient), indicating that part of the scatter is embedded in the ice itself. found seasonal peaks with up to 10–25 % amplitude in TAC, so we can assume most of the scattering to be caused by seasonal cycles or interannual variability. If we do so, we average over more cycles with an increasing age interval covered in the 25 cm of the adjacent reproducibility samples. The measured variation should therefore decrease with 1/N, N being the number of years contained in one sample, and the five samples in each 25 cm interval provide us with information on the analytical error according to σmeasured2=σice2N+σanalytical2. If N approaches infinity we get an independent estimate of our analytical error. In Fig.  in the right panel we display the variation in the reproducibility samples vs. 1/N with the best linear fit. We get a y intersect (corresponding to N=∞) of 1.4 mL2 kg-2. If the square root is taken, this independent estimate leads to an analytical error of 1.2 mL kg-1, very close to the 1.3 mL kg-1 we calculated in Sect. .

Most of our TAC data (years 2010–2012) were measured using the above described method, while data obtained between 2002 and 2004, 287 samples in total, were measured with a slightly different procedure, as described in . The main difference is that at that time the evacuation step after loading the ice into the vessel lasted for 2 h instead of about 30 min, and the released air was expanded three times in sequence into a smaller, unchilled sampling loop for analysis. For those measurements the TAC was determined three times per sample and the analytical error of TAC was estimated as the standard deviation of the three measurements, leading to individual error bars for each data point with an average error of 2.86 mL kg-1.

The 2002–2004 and 2010–2012 data are slightly offset from each other, so a method to intercalibrate the two data sets was developed. Also, between the measurement periods of 2010, 2011 and 2012, minor changes in the instrument could lead to small offsets which have to be accounted for. Data pairs of corresponding sample depths in the NGRIP ice core from the different measuring periods were identified, the measuring period of 2012 was taken as a reference. Reference data points are compared with interpolated values of the other dataset. Only the data from 2010 could not be compared directly to 2012 because they cover different sections of the ice core, and hence the 2010 data set was compared to the 2011 data. The mean of the offset values is displayed in Table  together with its standard error. The age differences to the closest points of the reference values are also shown in Table , with the interpolations providing better results if the data points are closer to each other, as expected from the natural variability of TAC in the ice. Based on this comparison, the data from 2002 were shifted by 3.4 mL kg-1, those from 2004 by 6.1 mL kg-1 and those from 2011 by -2 mL kg-1. The 2010 data are not significantly different (1.2 ± 1.4 mL kg-1) from 2012, so no correction was made. This corrected melt–refreeze data set was used to compare with the vacuum-melt data and showed no significant offset, as described in Sect. .

Based on recent studies , small-scale firn density is known to correlate with Ca2+ concentrations in the ice representative of mineral dust concentration. Accordingly, a firnification effect of dust on pore volume has been proposed , which should be most pronounced for stadial–interstadial variations when dust concentrations in Greenland changed by a factor of about 15 . As the TAC is a result of the competing process of densification and water vapor transport/recrystallization, an influence of Ca2+ concentration on TAC could also be hypothesized. In Fig.  the NGRIP TAC, dust and Ca2+ , CH4, and δ18Oice records are shown on the depth scale for selected DO events. No simple relation from TAC with the dust concentration can be observed. Moreover, the TAC variations on their depth scale are not in phase with dust and Ca2+ concentrations, as would be expected from a direct firnification effect of dust concentrations in the ice matrix on pore volume at bubble close-off. Instead, the high-frequency variations in TAC seem to change in parallel with CH4 and therefore on the gas age scale, suggesting a direct influence of temperature on the number of moles of air enclosed in the pore volume during bubble close-off. We will discuss this anti-correlation in the next section.

The TAC data (Fig. ) not only show low-frequency variations as discussed in Sect.  but reveal a strong high-frequency signal. Making use of the unprecedented resolution of our record, we investigate the high-frequency variations and take a closer look at what happens to the TAC during DO events.

The temperature effect (Eq. ) on the pore volume created during steady-state densification would lead to a very small increase in pore volume with rising temperatures. Using the ideal gas law, we obtain TAC=Vmol⋅n=Vmol⋅Pc⋅Vc(Ts)R⋅Ts=Pc⋅VmolR⋅(0.76-57KTs), where Vmol is the volume of one mol at STP, Vc(T) the pore volume at close off, R the gas constant (8.31 J mol-1 kg-1), Ts the snow temperature and n the number of moles of air enclosed in the bubbles. Therefore, a slight increase in TAC with increasing temperature is expected from the pore volume effect. However, the formula for pore volume changes, derived in based on steady-state Holocene conditions, is most likely not applicable during DO events where a transient change in densification occurs. It is reasonable to assume that the pore volume in the firn does not follow this temperature relationship (Eq. ) directly at the onsets of DO events. If we assume that the pore volume remains constant during the very first stage of a DO event, the first-order effect of slowly increasing temperatures in the firn would lead to a decrease in TAC, as supported by our data (Fig. ). To test objectively whether there is a coherent pattern of decreasing TAC at the onset DO events, we developed a method to find significant TAC decreases. To remove noise in the TAC raw data, 1000 Monte Carlo splines (varying the data points randomly within their error before calculating each spline fit) with a cutoff period of 750 years were calculated on the AICC2012 gas age scale, and the mean of the 1000 splines was taken as our best-guess representation of true TAC variations (Monte Carlo average, MCA). This MCA spline is then searched for maxima and minima. A detected minimum is considered significant if the difference between the last maximum and the minimum is larger than 1.5 times the added standard deviation of the spline at both points. The result is shown in Fig. . With these criteria and parameters, the routine finds 23 significant minima, of which 17 are related to a DO event in δ18Oice. The significant minima unassociated with a DO event occur at the onset of the Younger Dryas, two in the LGM and one during DO event 25. There is another one before DO event 24, which is due to a wiggle in the spline fit, leading to two significant minima in the descent preceding DO event 24 (see Fig. ). Using the abovementioned parameters, the routine fails to find significant minima related to DO events 8, 9, 16–18, 20, 22, 23 and 25, although for many of these cases a decline in TAC exists, which, however, did not satisfy our significance criterion. For DO events 9, 18 (and the event p18, in Fig.  regarded as a precursor event of DO event 18), 20, 23 and 25, this is due to the threshold of 1.5σ being too high, while 16–17 follow each other very closely so the TAC response signal is not visible. For DO event 22 the detected minimum is more than 1000 years before the δ18Oice maximum, so we considered this not to be related to the warming. DO event 22 has a small amplitude in δ18Oice compared to the background and the other DOs; thus, only a small TAC response is expected.

Apparently, TAC shows an anti-correlation not only to ISI but also to rapid DO warmings. Again a comparison to the O2 / N2 ratios is of interest, since found not only a correlation of O2 / N2 to insolation but also a correlation of O2 / N2 ratios with DO warmings. We speculate that both proxies are influenced by the same not yet fully understood firnification processes. The phasing of the TAC compared to the δ18Oice is also of interest. In Table  the timing of the TAC minima on the AICC2012 gas age scale and the maxima in the rises of δ18Oice on the AICC2012 ice age scale are shown. On average, the TAC minimum is synchronous with the δ18Oice maximum within the error (12 ± 290 years) on the AICC2012 age scale. However, as stated by , the AICC2012 gas age scale suffers from inconsistency with the AICC2012 ice age scale for several DO events as gas and ice have been synchronized between different ice cores to some extent independently. This leads to a dephasing of CH4 and δ18Oice records in some cores on the AICC2012 age scale, which is absent in the original age scales, where gas age scale has been determined by adding the gas-age–ice-age difference to the ice age scale. For this reason published a new gas age scale for NGRIP, based on the ss09sea06bm ice age scale, defined from 10 to 120 ka. Being aware of this inconsistency, we also derived the corresponding δ18Oice maxima on ss09sea06bm ice age and the TAC spline minima on the gas age scale by . On those age scales the δ18Oice maximum is reached on average 111 ± 232 years earlier than the minimum in TAC and only two DO events show the TAC minimum earlier than the δ18Oice maximum. Neglecting DO 13, the δ18Oice maximum leads TAC by 162 ± 108 years (37 ± 217 years on the AICC2012 age scales). Due to the considerable analytical and small-scale scatter of our TAC data, it is difficult to pinpoint the temporal evolution of the TAC and its phase relationship to other climate proxies in the ice core for individual DO events. Moreover, when comparing δ18Oice in the ice matrix and a direct temperature-related signal in TAC, the uncertainty in the ice-age–gas-age difference has to be taken into account. Therefore, in the following we compare the TAC behavior to other proxies only on the same age scales.

To figure out how the TAC reacts in general to DO event warmings, we calculated a stack of TAC variations during DO events and compared it to other gas phase parameters. Since the TAC seems to react in the time window where CH4 also shows changes, we stacked the TAC around the CH4 onsets. For this we defined a criterion for the rise in CH4. The analytical error in the CH4 data is 5.9 ppbv . The start of the CH4 increase was defined by in the middle between the first two data points during the onset of stadial–interstadial transitions which did not agree within their 3σ uncertainty anymore. We used the same definition and translated the depth values on the AICC2012 gas age scale. Additionally, we defined the onset for DO 3 and 22 by applying only a 2σ criterion, since with 3σ, no onset could be defined. These criteria give the onsets given in Table , except for DO 2 and 25, for which the onset could not be defined. The same stacking analysis was performed for δ15N , indicating temperature gradients across the firn column caused by rapid warming at the surface. The TAC (this study) and the δ15N time series from were then cut out in age windows +400 and -1000 years around the DO onsets in CH4. For each window we subtracted the mean value over this time span to remove the long-term trend in the data. Note that we ignored the temperature effect on pore volume as discussed in Sect. , as this effect is small (Fig. ) and does not occur in the gas itself but acts on the firn matrix. Due to gas-age–ice-age difference, the latter process is, therefore, not in phase with changes in temperature but affects TAC several hundred years later. The resulting data were then stacked and for each of them – the CH4, the TAC, and δ15N data – a spline with a cutoff period of 200 years was calculated. The result is displayed in the left panel of Fig. . Relative to CH4, the measured TAC decrease starts around 100 years earlier. Within the error, δ15N starts to increase synchronously with TAC. This 100-year lag of CH4 to temperature is somewhat more than the 25–70 ± 25 years calculated for DO events in Marine Isotope Stage 3 in previous studies and clearly more than the 4.5-24+21 years for the Bølling–Allerød interstadial (BA) calculated in . This difference may partly be attributed to the different methods used in the various publications to detect the onset in the CH4 rise and/or may be specific to the BA warming. Note that the stacked TAC data show a two-step decrease that lasts for several hundred years. When the δ15N signal reaches its maximum, TAC is still decreasing; shortly before the δ15N stabilizes, the TAC slightly rises and then drops in a second step to lower values than before the event.

The total amplitude of the TAC response in Fig. a is -4.7 ± 0.7 mL kg-1. Using Eq. () with all parameters but the temperature fixed, we can calculate the expected physical TAC response according to the ideal gas law (Fig. b). The temperature influencing the TAC is the bubble close-off temperature, as derived by using a heat transport model with the surface temperature determined by δ15N thermodiffusion thermometry. To get an average behavior of bubble close-off temperature, we also stacked this modeled firn temperature at bubble close-off for the DO events in windows of +200 to -800 years relative to the onset in close-off temperature (see Table ). We then calculated the mean over 50-year intervals from +175 to -775 year around the starting points of the temperature increase at bubble close-off (red points in Fig. b). The starting points were defined as the onset in bubble close-off temperature provided by on a depth scale, translated to the AICC2012 ice age scale. With a starting temperature and TAC of 227.15 K and 90 mL kg-1, respectively, we computed the expected TAC response (blue crosses in Fig. b). Also shown in Fig. b are the measured TAC values on ice age scale for comparison with the modeled TAC and the temperature at the surface. The calculated amplitude of the direct temperature effect through the ideal gas law (number density of molecules per volume) at bubble close-off is 1.4 mL kg-1, which is only about a third of the measured one. The amplitude difference indicates that other effects than the temperature at bubble close-off influence TAC on short timescales and especially during the second step of the TAC decrease, where in situ gas temperature changes are already quite small.

One possibility of explaining the larger TAC amplitude than expected from the direct temperature effect could be co-occurring changes in surface pressure, for example related to synoptic pressure pattern changes related to DO events. To explain the full amplitude in DO event TAC changes, however, a pressure decrease at the NGRIP site of around 17 hPa would be required during interstadial warmings, potentially related to a northward shift of North Atlantic storm tracks connected to a drastic reduction of sea ice during DO events which would also lead to a lowering of synoptic pressure over Greenland . However, compared to currently observed spatial gradients in mean annual sea level pressure over the North Atlantic, the size of this effect appears too large and, moreover, should occur synchronously with the onset of the DO events and thus is unlikely to explain the TAC changes in later stages of the DO events. In contrast, a transient effect of changes in firnification, hence pore volume, during Greenland interstadials appears more likely to explain our observations. We suggest that such an effect can be induced by the rapidly increasing accumulation rate at the onset of the DO event. This leads to a higher load and thus enhanced deformation of the snow grains at depth at a time when the temperature in the firn column is still cold. A simple transient firnification model experiment (Sect. ) supports this hypothesis by reducing TAC by several milliliters per kilogram as in our observations. In the following we attempt to quantify an upper limit of this transient firnification effect using a standard firnification model .

Empirical equations for estimating bubble close-off densities and bubble close-off depths have been derived for steady-state conditions (). However, especially at the beginning of a DO event the firn layer is far from being in a steady state condition. Fast artificial densification experiments of snow by applying high pressures resulted in very low TAC compared to natural firnification (B. Stauffer, personal communication, 2015). The reason for low TAC in artificially densified ice is most likely that, due to the extremely high densification rate, there is not enough time to form spherical cavities, which are a result of minimizing surface energy by slow mass redeposition through vapor diffusion. At the beginning of a DO event, accumulation increases in a step-like fashion, causing (less drastically but analogous to the artificial experiments) additional pressure in the bubble close-off zone by the increasing load of snow. We therefore expect a pore volume reduction and expulsion of air from the firn, yielding to lower TAC compared to steady-state conditions.

We estimate the upper limit of this effect by assuming that for some 140 annual layers above the firn–ice transition in the firnification model, the time required to reach bubble close-off remains unchanged after a transition to a DO event. This assumption is based on the fact that the temperature at the depth of bubble close-off remains near the cold state during the first 140 years of a DO event (less than 20 % temperature response compared to the surface temperature change; Fig. ) and on the hypothesis that time is more important for finalizing the bubble close-off than the additional hydrostatic pressure.

We have used a standard dynamic firn densification model to calculate this upper limit for a typical DO event. In addition to computing the time and depth where the steady-state close-off density is reached (as in the normal usage of the model) the model provides the density that a firn layer reaches after a certain number of years. This number of years was set to the duration needed to reach close-off under interstadial conditions. Under the abovementioned assumption of an initially constant duration to reach close-off, this density reflects the true close-off density and corresponding TAC better than values obtained for steady-state stadial conditions. Stadial temperature is set to -46 ∘C and the ice accumulation rate to 0.05 m a-1. At the beginning of the simulated DO event, we increase the temperature from -46 to -36 ∘C and the ice accumulation rate from 0.05 to 0.1 m yr-1 within 100 years, based on the model data by . The resulting TAC of the simulation is shown in Fig. . We interpret the resulting decrease in TAC as the upper limit scenario for the first 140-years of a DO event. The real effect might be smaller. Later, when the temperature at the firn–ice transition increases further, TAC will slowly approach the new equilibrium value. As there exists no physical model describing this dynamic behavior of densification and bubble close-off to date, we cannot provide a more precise modeled evolution of TAC during a DO event, but the decrease in TAC as observed in the NGRIP ice core seems to be compatible with the simulation.