Ancient atmospheric air is embedded in polar ice caps, making them a major source of data for reconstructing past climates . For example, the EPICA community traced climate variability back to 800 kyr before present from ice cores drilled at Dome Concordia (also named Dome C). The firn layer (approximately the first 50–100 m of the ice cores) is paramount in tackling the reconstruction of past climates, as the gradual densification of snow to ice leads to air entrapment. This firnication can last from a few centuries to a few thousand years before pore occlusion, with the consequence that the entrapped air is younger than the surrounding ice at a given depth . Unambiguously linking gas composition (from the air) and temperature evolution (from water isotopes in ice) in past climate conditions is challenging. In addition, the progressive closure of pores usually leads to a broad distribution of the trace gas ages. Seasonal layering of the polar firn also influences this closure e.g.,. In other words, the precise evaluation of the gas–ice age difference (Δage) requires a detailed understanding of the densification and gas trapping mechanisms.

A further complication is that, although the firn undergoes a similar densification with depth until it converts into solid ice, each polar site exhibits peculiar characteristics (local temperature, accumulation rate, impurity content, topography, etc.). Thus, climate proxies and air dating strongly depend on the polar sites investigated and there is now substantial literature that proposes multi-site studies .

The firn column is classically divided into three distinct zones . When considering air circulation, a convective zone, where gases are mixed with the atmosphere in the top layers due to the high permeability of snow and/or the effect of wind, is first encountered. Deeper in the firn, in the diffusive zone, molecular diffusion dominates and gravitational fractionation also occurs. The lock-in depth (LID) is defined as the depth at which gravitational fractionation stops . In the deepest firn zone named the lock-in zone (LIZ), the transport of gases in open pores becomes limited and eventually stops because pores close and entrap air. At the bottom of this zone, the close-off depth (COD) is the depth at which pores are fully isolated from the surface and at which air cannot be pumped out of the firn anymore.

Successive densification mechanisms appear along the firn column. Snow undergoes grain rearrangement, fracture, and sintering until a critical density of 550 kgm-3 is reached . This density corresponds to an approximate porosity of 40 %, close to the porosity that characterizes a random close pack (RCP) of spheres . As for many other granular materials, further densification requires the plastic deformation of the grains themselves. Above 550 kgm-3, dislocation creep becomes the dominant mechanism for densification . The last stage of densification is porosity related. When the density exceeds about 840 kgm-3, pores are closed and further shrinking is driven by the difference between their internal pressure and the larger surrounding stress.

The mechanisms of pore closure in deep firn are of interest in order to understand the relationship between atmospheric signals and trace gas records in firn and ice. Models of gas transport in firn generally include a parameterization of the closed-to-total porosity ratio e.g.,. However, only a few closed porosity datasets are available . Moreover, some recent studies emphasize the effect of firn layering, further motivating microstructural studies e.g.,.

The ratio of closed to total porosity may be obtained using two different techniques: pycnometry e.g.,, and X-ray-computed tomography e.g.,. Air content measurements are generally performed with melting–refreezing techniques used on samples taken well below the bubble closure zone and used as a proxy of the average air isolation density e.g.,. Recently, measured air content in the LIZ of the WAIS Divide ice core and used it as an indicator of the bubble closure rate. Each technique comes with its own issues. Air content measurements, when performed on firn samples, may artificially open some closed pores that are weakly sealed and melting–refreezing is a destructive technique that forbids any further microstructural investigation . Pycnometry only provides a bulk closed porosity value without information on pore morphology. X-ray tomography scans a rather small volume of firn, thus questioning the representativeness of measured properties . These three techniques all have the issue of border effects in common. In particular, one has to make assumptions on the closed or open status of cut pores. Regarding this issue, the effect of cut pores seems nonetheless much smaller in the case of air content data obtained from bubbles well below the LIZ e.g.,, than in the case of pycnometry or closed pores digitized by X-ray tomography on firn samples taken in the LIZ.

The X-ray tomography technique has received increasing interest in the last 20 years for investigating snow and firn microstructure e.g.,. Focusing on the microstructural evolution that accompanies the closure process, demonstrated the potential of the method by investigating the density and closed porosity evolution along the firn core of Vostok. They uncovered significant discrepancies between the ratio of closed porosity calculated from absorption images and measured by pycnometry. They attributed these differences to the small scanned volumes (0.785 cm3) compared to those used when performing pycnometry measurements (100 cm3). reported that the stratification of firn has an effect on several properties such as structural anisotropy, crystal orientated fabric, and the total air content at Dome Fuji. Other Antarctic sites (WAIS Divide and Megadunes in East Antarctica) were also investigated. WAIS Divide exhibits a high accumulation rate and relatively warm temperature, whereas Megadunes is very cold, with a very low accumulation rate. performed X-ray tomography and permeability measurements on these firn cores. They concluded that the coldest site is characterized by a less tortuous pore morphology. Taking into account the strong layering exhibited in WAIS Divide, also proposed that the air flow in polar firn is mainly controlled by pore structure and not so much by density variability. Focusing on the Summit site in Greenland, closely studied finely grained layers in the firn. Their results indicate that the ratio of the number of closed pores to the pore volume is marked by a sharp increase that related well with the LID. also used such a parameter but no relation with the LID can be observed in their Fig. 7. In contrast to this index, the increase in the closed-to-total porosity ratio is in better agreement with the LID. Overall, the literature on firn tomography concentrates on studying the evolution of structural parameters (such as permeability) and their relation to gas transport within the firn. It also focuses on differentiating polar sites, or relating microstructure to deformation mechanisms. However, despite giving useful information for densification modeling e.g.,, these X-ray tomography studies do not provide an unambiguous prediction of LIZ and COD. To that end, the recent work of uses X-ray tomography to scan very large volumes of firn from three different polar sites. Their study depicts an abrupt closure of pores when reaching a critical porosity (around 10 %) that is independent of the temperature site.

More generally, for X-ray tomography to become a reliable reference technique for firn investigation, errors due to acquisition (voxel size or resolution), image analysis (image thresholding, labeling of pores), and sample variability (size and spatial heterogeneities) and their impact on the microstructural properties should be thoroughly studied. This effort has already started for modeling based on X-ray tomography images, whether for physical effective properties or for snow mechanics . For example, and modeled the firn permeability with a lattice Boltzmann technique on a layered firn column using X-ray images. These authors worked out a representative volume element for permeability, going beyond the sole density as performed by , for example.

In this context, here we investigate in detail the error sources that come with the process of X-ray tomography imaging on two East Antarctica firn cores originating from Dome C and Lock In (located 136 km away from the Concordia station towards Dumont d'Urville). We gather several microstructural parameters, such as density, closed-to-total porosity ratio, surface area, and anisotropy, in order to study the closure of pores. We are able to discriminate which parameters correlate to the COD, as defined by the ultimate firn air pumping depth.

The paper is organized as follows. Section  details the characteristics of the sites studied here. Section  focuses on the errors originating from reconstruction and image processing of tomographic scans. In Sect. , we investigate the scale effect and determine the errors generated for the main physical properties studied when decreasing the resolution in the tomographic scans. Section  focuses on the comparison among four different sites, with particular interest in the two sites studied in this work (namely Dome C and Lock In), along with the polar sites detailed in . Section  takes advantage of image analysis tools to compute refined microstructural parameters that characterize the pore network throughout densification.

Two sites in Antarctica are studied, Dome C and Lock In

Note that Lock In is a polar site and does not refer to the lock-in phenomenon.

Conducting a refined X-ray characterization and comparison of polar firn requires a correct estimation of possible errors. In addition to precision, several other sources of errors exist which do not have the same influence on the results. These errors can come from spatial heterogeneity, size of the ROI, image resolution, image processing, and labeling assumptions.

This section focuses on giving estimates of these errors for the important parameters studied: the density, the closed porosity ratio, the connectivity index, and the SSA. These errors depend on depth, except for the numerical ones from reconstruction and image processing for which we assume an independent relative value. Results presented hereafter can be useful for future tomographic studies that should advantageously include error and variability estimations.

In this section, we compare our data retrieved from Dome C and Lock In to those originating from WAIS Divide (West Antarctica) and Megadunes (East Antarctica) from , which were also analyzed with X-ray tomography. We focus on the closed porosity ratio and morphological parameters that can be compared for all four sites. We note however that the depth intervals probed for the WAIS Divide and Megadunes sites are smaller than ours. Temperature and accumulation conditions for WAIS Divide and Megadunes are listed in Table ; porosity closes at a much shallower depth, between 60 and 80 m for WAIS Divide and Megadunes, as indicated by Fig. a, than Dome C and Lock In. In contrast, pore closure occurs below 80 m for Dome C and Lock In. The Lock In site has a larger accumulation rate and is a bit warmer than Dome C but exhibits a deeper closure of pores. When plotting the percentage of closed porosity against density, Fig. b shows that all points fall approximately on a master curve. This supports the idea that the close-off arises on first approximation at a particular density. Note that the Megadunes site is peculiar, as a dune experiences continuous snow deposition on its sides and has an average of zero accumulation in “hiatus” zones .

Figure  shows three morphological parameters of interest (degree of anisotropy, surface-area-to-volume ratio of pores, and structure model index (SMI)) that can be compared for all four sites. The evolution of these parameters is shown against depth (Fig. a, c, e) and against density (Fig. b, d, f). These geometrical parameters provide valuable information on the pore network morphology that could be useful for the understanding of firnification.

Figure a, b show the degree of anisotropy that was determined using the BoneJ plug-in on the pore phase. This parameter is calculated using a 3-D mean intercept length method that directly works out all possible directions. An ellipsoid is fitted to the scaled intercepted points, giving eigenvalues for the lengths of the ellipsoid axes. The degree of anisotropy of the morphology is 0 for a fully isotropic structure and tends to unity when all objects are aligned along a direction. Figure a, b indicate that for all four sites, the degree of anisotropy is rather low (≤0.4), with a mean value on the order of 0.2. No clear trend is observable with depth or density.

The surface-area-to-volume ratio (S/V) of the pores is depicted in Fig. c, d. S/V may be seen as a good descriptor of the complexity of the pore network morphology. In the case of pores as shown in Fig. , pore roughness is similar for both sites (pore surfaces are smooth). Therefore, a less tortuous network leads to a smaller S/V value. In contrast with anisotropy (Fig. a, b) a clear difference is observable between Dome C and Lock In sites on the one hand and WAIS Divide and Megadunes sites on the other hand. Our data indicate a fairly smooth trend for the Dome C and Lock In sites, whereas the WAIS Divide and Megadunes sites show much more variability on a rather limited depth interval. characterized samples from both finely grained and coarsely grained layers. The microstructural differences that inherently come with fine and coarse grains should explain the variability observed in their results. Concentrating on the S/V ratio against density (Fig. d), and focusing on the limited common density interval (750–850 kgm-3), we note that WAIS Divide exhibits the most tortuous pore network. The Megadunes site leads to a pore network the S/V values of which are in between those of Dome C and Lock In, but again with a much larger variability. Although relatively limited, there is a clear difference between Dome C and Lock In, with Dome C consistently exhibiting smaller S/V values than Lock In, either for the same density or for the same depth. Thus, Lock In presents, for a given depth or density, a more tortuous pore network than Dome C. Dome C and Lock In S/V values follow approximately a linear increase with depth.

The structure model index (SMI) is a popular index in the bone research community which is implemented in the SkyScan software CT-analyzer (http://bruker-microct.com, last access: 19 July 2018) used by . It was also used to analyze snow metamorphism for instance . The SMI describes the shape of pores, with positive values for convex shapes and negative values for concave ones. The SMI tends to 0 for plates, 3 for rods, and 4 for spherical particles. Two different methods are available to compute the SMI: the SkyScan plug-in and the BoneJ plug-in with the Hildebrand algorithms . As highlighted by , the SkyScan plug-in consistently leads to smaller SMI values than the Hildebrand plug-in. For the sake of comparison with the data of , Fig. e, f show the structure model index (SMI) of the porous phase obtained with both methods. As for the SSA, the SMI is computed using the pore surface area. Consequently, uncertainties are negligible and not shown.

As for the S/V parameter, the SMI computed by (using the SkyScan plug-in) exhibits a much larger variability than ours. In other words, the pore shapes measured at WAIS Divide range from semicylindrical to nearly spherical for a rather limited span of depth (55–70 m) or density. In contrast, data points from Dome C and Lock In follow a clear trend, which suggests a simple evolution from rod-like to sphere-like shape for increasing depth or density.

We have checked that the difference between WAIS Divide and Megadunes on the one hand and Dome C and Lock In data on the other hand does not originate from the different methodologies used in the two groups by computing the SMI of Dome C and Lock In with the same plug-in used for WAIS Divide and Megadunes. As shown by Fig. e, f, the SkyScan plug-in leads indeed to smaller SMI values than Hildebrand algorithms. But this does not contradict the general picture that Dome C – Lock In and WAIS Divide – Megadunes sites differ markedly when considering the morphology of pores. In any case, we believe that the linear evolution observed in Fig. e, f for Dome C and Lock In is pertinent as it relates well with the change in pore morphology shown in Fig. .

In the preceding section, we have compared four different sites using available data from the literature. In this section, we take advantage of the collected 3-D images for Dome C and Lock In to compute refined geometrical parameters. They should bring new insights into the intimate structure of firn and its evolution, and are also useful properties that can be used for diffusion or permeability modeling.

We have chosen to plot these parameters as a function of density alone but their evolution against depth can be obtained by fitting the data points in Fig. . Figure  sums up and defines these parameters: medium chord length (Fig. a), chamber-to-throat size ratio (Fig. b), maximal path diameter (Fig. c), and connectivity index defined in Sect.  (Fig. d). The parameters in Fig. a–c have been obtained by using the commercial software GeoDict (https://www.math2market.de/, last access: 19 July 2018). Definitions of these parameters are given hereafter. Volumes DC-C12 and LI-C12 were used, as the software requires parallelepiped ROIs.

Figure a shows the medium chord length in all three directions. The corresponding sketch only illustrates the intercepts in the z direction. The intercept lengths are measured and averaged for each direction. For each density, the medium chord length can be considered isotropic because no preferential direction can be determined. Both DC-C12 and LI-C12 depict a linear decrease of about 50 % from 22.33 to 100.38 m of depth for Dome C. For a given density, the medium chord length of LI-C12 is always smaller than that of the DC-C12 volumes. This confirms the more complex shape of pore morphology for Lock In as observed in Fig. .

As for the S/V ratio (Fig. c, d), we note for Dome C a slight discontinuity of the medium chord length decrease with density at approximately 800 kgm-3. At this density, the medium chord length ceases to decrease. This discontinuity is difficult to interpret but may be linked to the pinching of the thinnest channels that arises at the start of the pore closure.

Figure b illustrates the ratio of the calculated chamber to throat pore size distribution for the 90th centile. Chamber pore size distribution is worked out using the granulometry over the whole sample, and the throat pore size distribution is obtained here by porosimetry on all sample faces, in the X, Y, and Z directions. Figure , images B and II clarify the throat and chamber concepts . The porosimetry consists of the introduction of a sphere from the top surface, thus mimicking the intrusion of liquid from the specimen surface. Each tested size of spheres in the sample is associated with the volume fraction covered by the set of spheres. In Fig. II, this is represented by a light blue area in which a particular sphere can circulate. When the space between pores is too small the sphere cannot move down anymore. This is different from the chamber pore size distribution, which is only based on the geometry of pores. Spheres of different sizes are placed in every available space of the porous network in that case. We chose to display the distribution at the 90th centile, as the porosimetry is difficult to perform for a deep sample. This provides the general trend in the closure of pores by pinching while still having large globular parts. Error bars show the standard deviations from the mean value of the porosimetry results on the six cubic faces. These are shown only for Dome C. After the air isolation density, there is a drastic increase in this ratio, as pinching reduces the throat size.

Percolation paths on subvolumes were calculated in the z direction alone. They are evaluated by moving the largest possible sphere inside the pore network, from the top surface to the bottom one. For each sample, 10 percolation paths were calculated, starting with a minimum path diameter of 24 µm and then increasing it by 24 µm steps. Figure c shows the calculated maximal path diameters. The vertical lines represent the variability based on all paths that are different, and the dots are the mean of those maximum diameters. A general decrease is observed, from approximately 300 µm at 550 kgm-3 to zero (i.e., less than 24 µm when reaching approximately 830 kgm-3), which is slightly lower than the air isolation density (840 kgm-3; ). Again, there are no noticeable differences between Dome C and Lock In. Both sites exhibit a large variability in the maximal path diameter that can vary between 0 and 200 µm in the same sample. However, these diameters are quantitative information for the path of air (in a given interval). A noticeable issue of this calculation is that the maximal path diameter depends on the size of the chosen subvolume. Here a cube of 6.72 mm in size was used, which ensures percolation until 830 kgm-3 according to Fig. . The length of the path ranges from 8 to 18 mm, meaning a tortuous structure whatever the depth. This is shown in image A in Fig. . A larger cube would have led to a drop in the maximum path diameter to 0 before 830 kgm-3 because of the structural isotropy of the pore network and the erratic process of closure. A smaller porosity amount is associated with a smaller probability of having a network connecting two opposite sample sides. Figure b, c do not allow for a clear differentiation between the DC-C12 and LI-C12 samples.

It is instructive to compare the evolution of the connectivity index in Fig. d to that of the chamber / throat and maximal path diameter (Fig. b–c). The air isolation density obtained by for Dome C is well correlated to the end of the drop of the connectivity index (black dashed line). It also correctly separates the two regimes observed in Fig. b, c.

Figure  compares the evolution of the connectivity index with depth for Dome C and Lock In. When the connectivity index drops to very small values, Fig.  clearly shows a sharp change in the slope for the two sites. As for Fig. d, three stages can be clearly distinguished with two horizontal parts and an abrupt linear drop. The last two linear portions of the curve intersect at depths that are in good agreement with both the ultimate depth at which air could be sampled and with the parameterization of air isolation depth related to air content data of . The parameterization is used for temperatures of Dome C and Lock In.

Indeed, the blue and red solid lines correspond to the ultimate air pumping depths at Dome C (99.5 m) and Lock In (108.3 m) (see Table ), whereas the blue and red dashed lines correspond to the parameterization of the air isolation density related to air content measurements, called close-off density in . The air isolation depth was calculated from our measurements of density (Fig. ). Using the connectivity index evolution thus seems a promising method to locate the depth and density at which pores are nearly fully closed. Its main advantage is that it does not depend on assumptions or arbitrary choices on the status of pores (closed or open). According to Fig. , the end of the connectivity index drop down at Lock In is approximately 8 m below the one of Dome C, consistent with the difference in last firn air sampling depths between these sites.

Although exhibiting a size distribution, grain size measurements showed a larger mean grain size at Dome C than at Lock In. Near the close-off depths of Dome C (100 m) and Lock In (108 m), the mean cross-sectional area was measured from thin sections to be approximately 1.78 and 0.59 mm2, respectively. We observed that grains in the Dome C firn increased in size with depth (from 0.57 mm2 at 60 m to 1.78 mm2 at 100 m) while grains in the Lock In firn showed no clear increase in size in the probed depth range (60–120 m). Figure  compares two thin sections of firn from Dome C and Lock In for the same density. This illustrates the clear difference in grain size between these two sites. This information on grain size, together with that on medium chord length (Fig. ) and surface-area-to-volume ratio (Fig. ), suggest a more tortuous pore structure for Lock In.

X-ray characterization of firn samples was performed for two polar sites, Dome C and Lock In, over a broad depth range. We focus on the microstructural markers that accompany the closure of pores. The most obvious method to characterize pore closure is to measure the ratio of closed to total porosity. However, building on a thorough estimation of the results' accuracy after imaging and processing, we have shown that this approach has serious drawbacks as the percentage of closed porosity exhibits large variability with sample size and voxel size and spatial heterogeneities when characterized by X-ray tomography. This is problematic since most models of air transport in the firn such as , , , and rely on a diffusion coefficient that requires the knowledge of the evolution of the closed porosity with depth and/or density. Thus, these models depend on a correct parameterization of the volume fraction of closed pores and there is no consensus on those that have been proposed . The cut-pore effect also has to be taken into account on the boundaries of the sample.

Here, we have encountered similar difficulties in unambiguously determining the fraction of closed pores. For example, we have determined that near the critical density of 840 kgm-3, it ranges from approximately 20 to 80 %. This uncertainty results from the conjunction of three detrimental effects: the sample size, the voxel size (resolution), and an inherent spatial heterogeneity.

We propose an alternative parameter: the connectivity index, which is simply the volume of the largest pore divided by the total pore volume. The main advantage of the connectivity index is that it is much less sensitive to cut pores that undermine the measure of the closed porosity ratio. Before the close-off depth (COD), the connectivity index is essentially affected by horizontal spatial heterogeneities in the sample but not much by resolution and sample size. When focusing on the determination of the COD, we have shown that a sample size on the order of 1–2 cm3 is a reasonable choice for the connectivity index determination. In these conditions, the connectivity index accurately predicts the COD as defined by the ultimate air sampling depth for the Dome C and Lock In sites. It also agrees with the parameterization of related to the air content measurements from . When using tomographic data, we propose using the connectivity index to precisely determine the COD.

That being said, the two sites studied in this work (Dome C and Lock In) are both characterized by cold temperatures and low accumulation rates. It would be interesting to use the connectivity index at other polar sites to confirm its relevance for COD determination. Indeed, further challenging this index at polar sites exhibiting layering such as WAIS Divide would help in determining if this metric is appropriate to characterize closure.

In comparison to our work, took advantage of X-ray scans on slices 4 cm in height and of the full core diameter to determine the status of subvolume pores (closed or opened). Section  discussed the effects of the voxel size by comparing results from samples using 12 and 30 µm. The difference for the closed porosity ratio was less than 7 %. Therefore, results obtained by with a voxel size of 25 µm should not be too vitiated by voxel-related errors. However, their definition of a closed pore still necessitates the knowledge of the status of the surrounding pores. This requires having access to larger volumes than those studied. In our work, only three samples have the diameter of the core. In addition, as detailed in Sect. , the voxel size of the largest samples has a great influence on the fraction of closed pores. The large samples and voxel size used by seem appropriate to reasonably limit cut-pore effect without suffering too much from voxel size issues. However, it is still hindered by the unavoidable possibility of having a large closed pore (larger than the sample) that is wrongly considered open. The use of the connectivity index avoids these issues.

The morphology of pores was compared to data from for polar sites WAIS Divide and Megadunes. Their data show more variability than ours, which can be explained by the selection of finely and coarsely grained layers and the different nature of the studied sites. Indeed, Dome C and Lock In are very cold sites with low accumulation, with Dome C at the tip of the dome. In contrast, Megadunes is a site exposed to strong winds that redeposit snow from one side of the dune to the other, thus leading to a non-steady-state site. WAIS Divide is a warmer site with a high accumulation rate. Layering is significant, and high-density layers of fine grains can be found above low-density layers of coarse grains. As intentionally extracted samples both from coarsely and finely grained layers, and plotted their data indiscriminately with bulk density, these led to more dispersed results. Using a local density (density of the scanned sample rather than the density of the whole sample) as done here could have reduced the dispersion of their results as discussed by . Such a strategy could have helped confirm or reject that close-off occurs at a critical density as suggested by , while current inaccurate estimations do not allow such a claim. Again, we believe that the connectivity index would clearly answer this question and would discriminate the role of the density and of the microstructure on closure if all curves fall on a master curve.

The polar sites Dome C and Lock In were extensively compared. Shapes of pores, closed porosity, and connectivity indices likewise evolve with density. However, the closure of pores occurs deeper for Lock In than for Dome C (by 8 m). Our results on the medium chord length, the surface-area-to-volume ratio, and grain size suggest a more tortuous firn at Lock In than at Dome C. This could have interesting implications for air diffusivity in the firn at these two sites. If Lock In is more tortuous, older air samples should be retrieved from firn air pumping.