In the mature ice phase below the close-off depth we observe significant decimetre-scale variability in the CH4 records of every ice core analysed. In each case, it is impossible that this high-frequency signal could have existed in the atmosphere at the ice sheet surface and survived the low-pass filter action of the firn – the gas age distribution widths (Table 1) are greater than the approximate signal periods. We initially focus in detail on only Tunu13 and B40 because these are the most complete records, with relatively little ice removed prior to analysis and few ambient air entry problems, both factors linked to the number of core breaks (Table S1).

A smoothing spline is subtracted from the CH4 record of each site to effectively remove the atmospheric signal (Fig. 3a and b, Tunu13 shown). The residual CH4 record contains a high-frequency, non-atmospheric signal and analytical noise (Fig. 3b). The mean peak-to-peak amplitude (see Supplement) of the residual high-frequency CH4 in the Tunu13 record from 987 to 1870 AD gas age is 5.3 ppb (median is 3.7 ppb) and varies between 2 and 42 ppb. Variability of similar peak-to-peak amplitude and frequency observed along the NEEM ice core continuous CH4 profile was attributed to analytical system noise (Chappellaz et al., 2013). Here, we have confidence that we capture a high-frequency signal present above the analytical noise in some sections of the record because discrete CH4 measurements on the Tunu13 core conducted at 6 cm resolution also show substantial variability within each 15 cm depth section. CH4 concentrations in adjacent samples differ by up to 32 ppb, but more typically by 3.4 ppb, and reproduce some of the decimetre-scale changes resolved by the continuous measurements (Fig. 3c–e). CH4 oscillations captured by the discrete measurements are larger in amplitude than those in the continuous gas record because the continuous gas analysis system causes more signal smoothing than the discrete analysis (Stowasser et al., 2012; Table S1, Fig S2). The 5.3 ppb mean peak-to-peak amplitude of this high-frequency non-atmospheric signal must therefore be a minimum estimate of the true signal in the ice.

A high-frequency, non-atmospheric signal in excess of analytical noise is also present in sections of the B40 continuous CH4 record and it is reproducible; we measured replicate ice core sticks on different days and were able to resolve very similar decimetre-scale features in ice samples from 114–120 m depth (Fig. 4). The sharp CH4 troughs at 122.8, 122.6, 122.3, 121.3 and 120.2 m are particularly well replicated and highly unlikely to be analytical artifacts. The mean peak-to-peak amplitude of the high-frequency non-atmospheric signal in this section of the B40 record is 5.4 ppb (median is 5.1 ppb).

Our results demonstrate that the quasi-annual variability previously observed in the ice phase of the NEEM-2011-S1 core (Rhodes et al., 2013) is not unique to NEEM or to Greenlandic ice. The question now is: what causes it? If it is an artifact of layered bubble trapping, as speculated for NEEM-2011-S1, the observed decimetre-scale variability should respond in a predictable way to several factors that vary over time and between ice core sites. We therefore systematically examine our empirical data to assess the influence of each factor and judge whether any relationship is consistent with the mechanism of layered bubble trapping.

Our conceptual model of layered bubble trapping predicts that the difference in CH4 concentration between adjacent layers (ΔCH4) should increase with the CH4 concentration gradient in the firn column, which is dictated by the atmospheric CH4 growth rate (Fig. 1). We can clearly observe this relationship in the Tunu13 record; amplitudes of the decimetre-scale CH4 oscillations are greatest when the atmospheric CH4 concentration shows a sustained trend of increase or decrease, particularly during the steep post-Industrial Revolution CH4 rise and the growth and decay in atmospheric CH4 concentrations associated with the prominent CH4 oscillation centered on 1550 AD (Fig. 3b).

To explore this relationship quantitatively, we compare the CH4 growth rate to the standard deviation (σ) of the high-frequency CH4 residual (data minus spline, as Fig. 3b) for moving windowed sections of the Tunu13 record. Windows are 40 years in length and are calculated at 10-year interval. Strong linear relationships between CH4 growth rate and the magnitude of high-frequency variability are revealed for atmospheric CH4 growth and decay rates > 0.4 ppb yr-1 (Fig. 5e). The gradients of the linear relationships are similar in both cases (7–8 ppb σ-CH4 ppb yr-1 growth rate). At low growth rates (< 0.4 ppb yr-1)σ-CH4 values reflect the analytical precision of 1.7 ppb. The observation that σ-CH4 only increases beyond analytical noise at growth rate > 0.4 ppb yr-1 heavily implicates the mechanism of layered bubble trapping as the cause of the high-frequency CH4 signal because it requires sustained trend of change in atmospheric concentration to produce CH4 artifacts (Fig. 1). We therefore define high-frequency non-atmospheric CH4 variability in excess of analytical noise as “trapping signal”.

This analysis was repeated on the high-frequency CH4 residual records from other ice cores: B40, NEEM-2011-S1, D4 and NGRIP (Fig. 5a–d). For NGRIP, only data from 1050–1240 and 1774–1860 AD (gas age) were used, the latter with a 10 years length window to avoid data gaps. For NEEM-2011-S1, data from 1450–1840 AD were used. Any 40-year time window with a data gap > 5 years duration was discarded from analysis. We note that the CH4 growth rate recorded in the ice core is not strictly equivalent to the atmospheric growth rate because firn-based smoothing may have caused some damping of the signal (Fig. 2). The B40 record is significantly affected by firn-based smoothing (Fig. S2), which reduces the growth rate captured by the ice core archive. The B40 record is also severely impacted by system-based smoothing (Fig. S2), which damps the trapping signal to within range of the analytical noise for much of the record, except the section displayed in figure 4. The combination of these two effects destroys any relationship between atmospheric growth rate and amplitude of the high-frequency signal (Fig. 5a). There is also little sign of a relationship between growth rate and σ-CH4 in the NEEM-2011-S1 data (Fig. 5b) and we speculate this is the result of a more aggressive ambient air screening method applied by Rhodes et al. (2013) that may have removed real variability.

Results are more encouraging for D4 and NGRIP as both sites exhibit linear relationships between CH4 growth rate and the trapping signal magnitude (Fig. 5c and d). Both negative and positive growth rates at NGRIP exhibit the same gradient of change with σ-CH4. The consistency of results between sites is important for the identification of layered bubble trapping as the mechanism behind the high-frequency variability. Further support can be drawn from the CIC firn air transport model, which predicts a linear relationship between atmospheric growth rate and the CH4 trapping signal magnitude at WAIS Divide (red line, Fig. 5f). When the Tunu13, D4 and NGRIP data are all plotted on the same axes with the WAIS Divide model simulation (Fig. 5f), the gradient of the modelled linear relationship is within the range of gradients of our empirical data from three different Greenland ice core sites. Clearly, the CH4 trapping signal magnitude (σ-CH4) does not have the same sensitivity to growth rate at all ice core sites; another factor is influencing CH4 variability, as we explore below.

For completeness we note that physics tells us that there can still be a tiny layered bubble trapping signal at zero growth rate due to the effect of gravity. As CH4 is lighter than air, gravity reduces the CH4 concentration with depth relative to the concentration in the atmosphere. Thus at zero growth rate there is still a CH4 gradient in the firn that can result in the generation of a trapping signal via layered gas occlusion. This also means that at positive atmospheric growth rates, the gravitational gradient must be overcome in order to generate CH4 oscillations related to layering. This is why the modelled WAIS Divide growth rate vs. σ-CH4 plot intersects the x-axis at a slightly positive growth rate and σ-CH4 is predicted to be 0.11 ppb at zero growth rate (Fig. 5f). This effect is an order of magnitude smaller than the analytical noise and is not detectable.

At a constant atmospheric growth rate, the CH4 trapping signal amplitude produced by layered bubble trapping should be determined by the difference in age between the air trapped relatively early compared to younger air trapped relatively late (t2 minus t1 on Fig. 1). One factor that will affect how quickly an adjacent layer is closed off is accumulation rate (A) – more new snow accumulation will cause layers to spend less time in the firn column reducing the time interval over which layered bubble trapping can occur. We test this hypothesis by comparing the CH4 trapping signal magnitude in ice cores with different accumulation rates (Fig. 6a and b). Comparison is performed for two discrete time periods (gas age) for which we have good quality CH4 residual data (continuous and above analytical noise) from three cores, and we assume all three sites experienced the same atmospheric growth rate. As expected, there is a significant decrease in σ-CH4 with increasing accumulation rate for the 1770–1900 AD time period (Fig. 6), but the 1490–1630 AD interval shows no trend (Fig. 6a).

However, if we adjust the σ-CH4 values of each ice core to compensate for the differences in the smoothing effect of the analytical system, the results from the two time intervals become more consistent (Fig. 6c and d). To perform this adjustment, we assume that the high-frequency signal has an annual periodicity and consult the Bode plots generated from switching the analytical system between two gas standards, to determine what fraction of the original amplitude is retained by the system (Fig. S2). The nature of this relationship differs between time slices considered. An inverse relationship between σ-CH4 and annual layer thickness is identifiable for the 1490–1630 AD interval and a power law fit is applied, but a linear relationship would also be applicable here. A power law relationship is identifiable between annual layer thickness and σ-CH4 for the 1770–1900 AD time period, which has the greatest range of annual layer thickness and σ-CH4 values. These corrected data suggest that, at a fixed growth rate, an inverse relationship exists between accumulation rate and the magnitude of CH4 variability (σ-CH4). This is how we would expect CH4 trapping signal to respond to accumulation rate.

CIC firn air transport model simulations for WAIS Divide exhibit a similar power law relationship to the empirical data, whereby σ-CH4 is proportional to 1/A1.47. The slope is the result of two separate effects. First, increasing A decreases the time adjacent layers spend in the firn column, which by itself should cause CH4 trapping signal to scale as 1/A. Second, at increased A the advective gas transport in the open pores is enhanced, and this reduces the CH4 gradient down the firn column. If bubbles are then trapped over the same depth range, the amplitude of CH4 variability will be reduced, and this effect appears to scale as 1/A0.47 in the firn model. An important caveat is that the model assumes no change in the firn density profile with changing accumulation rate, which is unrealistic. However, the model does appear to capture a response of CH4 trapping signal to accumulation rate that is roughly comparable to that observable in the real-world data.

Another factor that should influence the amount of time that passes between early and late bubble closure is the degree of contrast between the physical properties of firn in adjacent layers. There is no doubt that the physical properties of firn ultimately control when a bubble is occluded, or a layer is completely sealed off. The relative importance of local density variability, firn microstructure, permeability and/or porosity in this process is actively debated. The traditional interpretation of density as the principal influence on bubble occlusion is being challenged (Gregory et al., 2014). However, we concentrate on the potential influence of local density variability in this section.

The controls on density layering in the firn are poorly understood, but a recent study suggests that variability near the firn-ice transition is higher at warmer, high accumulation sites (Hörhold et al., 2011). It is difficult to test the effects of density layering because we do not have the high-resolution density information required to do so. However, we can use the CIC firn air transport model, which utilises high-resolution density data for the WAIS Divide ice core, to make a prediction. In these simulations, we define the density layering to be ρlayer= ρ-< ρ> with the local firn densities (ρ) as given by the high-resolution measurements, and the bulk density (< ρ >) as given by a spline fit to those data. We then run the model several times with a density profile that equals ρ = < ρ> +αρlayer. By varying the scaling parameter α between 0 and 1.6 we can effectively control the magnitude of the firn density layering. As we would expect, no high-frequency CH4 trapping signal is produced in the absence of density layering (α= 0; Fig. S5). When the magnitudes of the local density anomalies are halved (α= 0.5), the trapping signal amplitude decreases slightly more than 2-fold from 7.3 to 3.2 ppb. This effect is minor compared to that of accumulation rate or atmospheric growth rate. However, it may explain why interior Antarctic sites, like B40, which have less pronounced seasonality in density at the firn-ice transition compared to coastal Antarctic or Greenland locations (Hörhold et al., 2011) may show only a moderate trapping signal despite the extremely low accumulation rates.

Having established that the high-frequency CH4 signal we observe in all the ice cores in this study shows characteristics consistent with the mechanism of layered gas trapping (Fig. 1), we are able to discern aspects of this physical process.

First, the CH4 trapping signal measured for the different ice core sites allows us to estimate the age difference between the air samples trapped in adjacent layers (t2–t1 on Fig. 1). High-frequency CH4 residual data, corrected for system smoothing effects (Sect. 3.4.2) from the 1810–1860 AD time interval, which has an atmospheric growth rate of 1.5 ppb yr-1 (in D4 – the least susceptible record to firn-based smoothing of the atmospheric signal), suggest a gas age difference between adjacent layers of 23 years at Tunu13, 2.4 years at D4 and 5 years at NGRIP. These values can be compared to previously published estimates of 10 years for WAIS Divide (Mitchell et al., 2015), 12 years for NEEM-2011-S1 (Rhodes et al., 2013) and 2 years for Law Dome (Etheridge et al., 1992). Unsurprisingly, the gas age difference between adjacent layers is greater at lower accumulation sites. To negate the issue of smoothing associated with the analytical system, we also consider Tunu13 discrete measurements, which show a maximum oscillation of 32 ppb amplitude at an atmospheric growth rate of 1.5 ppb yr-1 (Fig. 3c). The age difference between layers in this case would be 21 years, which is very close to the estimate above.

Second, the frequency of CH4 oscillations resulting from layered bubble trapping should reflect the difference in depth, and therefore also ice age (not the age of the gas trapped inside the bubbles, as discussed above) between adjacent firn layers where bubbles are closed off at different times. To test this with our ice core data we perform multi-taper method (MTM) spectral analysis of the Tunu13, D4, NGRIP and B40 CH4 records (Fig. 7). Spectral analysis is performed in the ice age domain because we believe that physical properties of the firn/ice are ultimately responsible for the high-frequency artifacts recorded in the gas phase at the same depth. Prior to analysis, the data in each 40-year window (as Sect. 3.4.2) are interpolated to an even ice age spacing that is twice the median sample spacing and any windows containing data gaps > 2 years are ignored. We then average the MTM spectra produced to generate mean spectra for sections of the record with relatively high or low growth rate, or in the case of D4, sections of the record encompassing only mature ice or some firn.

Sections of the Tunu13 record with CH4 growth rates > 0.4 ppb yr-1 exhibit spectral peaks at 1-year period in the ice age domain and the averaged spectrum for growth rates > 0.4 ppb yr-1 has a significant 1-year periodicity (95 % confidence) (Fig. 7). By contrast, sections of the Tunu13 record with growth rates < ±0.4 ppb yr-1 show no significant periodicity. The high accumulation Greenland ice core D4 shows an annual periodicity in CH4, but it only becomes significant when data from the lock-in zone are included (Fig. 7). NGRIP shows small spectral peaks at 1-year period for 2 out of 4 time windows with growth rates > 0.2 ppb yr-1 but the peak in the averaged spectrum is not significant (Fig. 7). Again, NGRIP data sections with growth rates < 0.2 ppb yr-1 exhibit no periodicity. No significant periodicity is resolved in the B40 high-frequency residual CH4 record, potentially because any annual signal has been removed by analytical system smoothing.

The significant annual periodicity resolved in the Tunu13 and D4 records during periods of relatively high growth rates strongly suggests that the mechanism of layered bubble trapping is linked to regular, seasonal variations in the physical properties of the firn pack, over a wide range of Greenland ice core site conditions. The quasi-annual high-frequency signal observed in mature NEEM-2011-S1 ice (Rhodes et al., 2013) could also be added to this list. We note that even if there is some ambient air contamination of D4 lock-in zone CH4 measurements, the wavelength of the CH4 oscillations in the lock-in zone should reflect the depth spacing of alternating layers with contrasting ratios of open to closed porosity, and therefore relatively more or less contamination (Fig. 7).

The regular oscillations between relatively young and relatively old air trapped in the ice core air bubbles suggest that the early-closure layers (ph on Fig. 1) are not sealing layers which prevent vertical diffusion. In other words, some degree of open porosity/permeability must be maintained in these early-closure layers to allow relatively young air to diffuse down through the firn pack towards the late-closure layers (pl on Fig. 1). This movement could be via vertical cracks or channels of open porosity tracking around isolated clusters of closed pores in the early-closure layers (Keegan et al., 2014). Furthermore, our results suggest that this situation must be maintained for upwards of 20 years at the Tunu13 site.

The onset of the lock-in or non-diffusive zone (Sowers et al., 1992) is commonly believed to be linked to horizontally expansive sealing layers. Field measurements of firn air (air pumped from the open porosity in the firn) provide strong evidence for such sealing layers by demonstrating a lack of vertical mixing within the lock-in zone. For example, halocarbon tracers linked to anthropogenic industrial activity are effectively absent in the lock-in zone firn air at many sites (Butler et al., 1999; Severinghaus et al., 2010; Sturrock et al., 2002). To first order, the trapping signal we observe in the ice cores therefore suggests that significant bubble closure in the early-closure layers must occur above the lock-in depth, where vertical diffusion of the relatively young air required to form the regular CH4 oscillations is not impeded. However, we do not rule out a contribution to the trapping signal from within the lock-in zone because (a) some vertical pore connectivity in the lock-in zone is required to explain firn air observations at NEEM (Buizert et al., 2012) and (b) air content of mature ice is not consistent with fully sealing layers at the lock-in depth (Martinerie et al., 1992). Measurements of WAIS Divide lock-in zone samples suggest that much of the trapping signal is inherited from bubble trapping above the lock-in depth, below which the signal gradually becomes muted as vertical gas mixing is limited (Mitchell et al., 2015).

Our results suggest that the variations in local density and/or other related physical properties, such as open porosity or grain size (Gregory et al., 2014) maintain an imprint of annual variability towards the base of the firn column that is strong enough to produce regular layering in the firn, resulting in a CH4 trapping signal with a significant annual periodicity. It is still not clear precisely how and why layering in polar firn evolves with depth and time in the way that it does. Hörhold et al. (2012) suggested that “impurities” which exhibit an annual cycle in concentration may act to promote densification by softening the impurity-rich winter firn layers. Hörhold et al. (2012) reported positive correlations between soluble calcium (Ca2+) concentration and local density but their choice of Ca2+ was not supported by any causal physical link between Ca2+ and densification rate. Ensuing work suggested that chloride (Cl-) and fluoride (F-) were more likely candidates to drive densification at NEEM (Fujita et al., 2014), drawing on early experiments which detail how substitution of Cl- and F- ions into the ice lattice promotes dislocations and causes a softening effect (Jones, 1967; Nakamura and Jones, 1970). A subsequent study confirms these ideas by demonstrating their application to the Dome Fuji ice core (Fujita et al., 2016). It is important to note that Fujita et al. (2016, 2014) also invoke a second, independent process that contributes to densification which involves textural effects and is related to depositional conditions.

Our data cannot resolve this issue, but we can use the chemical concentrations measured as a proxy for local density, assuming that winter/spring chemical species like Ca and Cl are enriched in the relatively dense layers. In the Tunu13 ice core, concentrations of Ca and Cl show significant negative correlation (p < 0.05) with CH4 anomalies when growth rates are positive (Fig. 8). A similar relationship is observable for the short section of the B40 core with significant CH4 trapping signal, using Na in place of Cl in this instance because it is easier to measure at very low concentrations (Fig. 4b). These observations confirm the seasonality of layered gas trapping that we have assumed – Ca and Cl-rich, dense, layers trap air earlier, preserving a relatively low CH4 concentration when atmospheric CH4 is increasing, and vice versa. Correlation between impurity levels in the ice and CH4 anomalies does not signify a causal link between them. It makes sense that the correlation between ice chemistry and CH4 is stronger at high growth rates because the trapping signal produced at these times has a relatively high amplitude and an annual periodicity. What is more interesting is that the sign of the correlation coefficient between Ca or Cl and the high-frequency CH4 signal switches when CH4 growth rate is negative rather than positive (Fig. 8). When atmospheric CH4 is decreasing, a Ca-Cl-rich layer that closes off early will trap air with a relatively high CH4 concentration. This is an important final piece of evidence to attribute the high-frequency CH4 signal in ice cores to layered bubble trapping.