Field location

Summit Camp is a year-round research camp located near the summit of the Greenland ice sheet at ≈72.58°N, 38.47°W. It is the site of an ice core drilled 3054m to bedrock, completed in 1993. The 30m boreholes used for this work are approximately 1 km away from the main camp. The mean annual temperature at Summit is –31 °C and the mean accumulation is ≈25cm a^–1 (ice equivalent) (Reference MeeseMeese and others, 1994; Reference Alley and WoodsAlley and Woods, 1996).

Field measurements

Neutron-scattering density probe

The density probe used for this experiment was a version of the Wallingford soil-moisture probe, adapted for use in measuring snow density as part of an IGLS (Reference Morris and CooperMorris and Cooper, 2003). The probe consists of an annular radioactive source of fast neutrons around a cylindrical detector of slow neutrons. Fast neutrons are emitted from the source. As they move through the snow, they lose energy by scattering. The count rate of slow neutrons arriving back at the detector per unit time is related to the density of the snow.

A calibration equation based on three-group scattering theory relates count rate to the density of the surrounding medium, given the borehole diameter and distance from the wall of the borehole (degree of centralization). Errors in the density can arise from deviations from the nominal borehole diameter and deviation from the nominal degree of centralization. These errors can be reduced if the actual borehole diameter is measured as a function of depth using calipers and if the neutron probe is held in position, either using a centralizer, or using a spring device to hold it against the wall of the borehole.

The emission of fast neutrons is a random process, so the relative error in the count rate decreases with a lengthened counting period and with increased source strength. Using a radioactive source small enough to be easily manageable in the field, logging speeds of ≈ 2cm min^–1 are required for cm-scale detail. In this case we use a speed of 7cm min^–1. The result of an IGLS log is a profile of density as a function of depth. Figure 1 shows the two logs plotted together.

Fig. 1. The density and optical profiles. Density is the black line and intensity is the grey line. Several features can be seen that are replicated in the two logs, particularly in the shallow region.

Filtering and correlation

We low-pass filtered all logs with a length-scale cut-off of 10cm to remove the effect of high-frequency noise. We calculated the correlation coefficient between the logs in windows of approximately 2.5m to assess the correlation between logs using different methods. These ‘windowed’ correlation coefficients are shown in Figure 2 and the data from each window are shown in Figure 3. As can be seen in Figure 2, the correlation is strongly positive near the surface; however, it decreases and finally becomes negative near the bottom of the borehole (approximately 30 m).

Fig. 2. Windowed correlations between density and intensity. At shallow depths, correlation is excellent, but deeper it fades. See Discussion for details.

Fig. 3. Windows for correlation. The data in each window are de-trended and scaled for display. Density is shown as a black line and intensity is shown in grey. The correlation coefficient for each window is shown. Depth in meters increases along the horizontal axis.

Wavelet correlation

Simple windowed correlation of the two datasets may fail to show some relationships between them if the data are nonstationary, as would be expected for annual layers, where layer thickness decreases with depth due to compaction. The size of the window chosen for correlation might then have a direct impact on the types of relationship shown by the analysis. This possibility was addressed by turning to wavelet methods, which naturally accommodate non-stationary data. As an alternative method for determining the scale-dependent correlation between two datasets, the correlation between wavelet coefficients at selected scales can be used (Reference Whitcher, Guttorp and PercivalWhitcher and others, 2000; Reference Cornish, Bretherton and PercivalCornish and others, 2006).

A wavelet transform decomposes a data series into a series of wavelet coefficients which represent the ‘power’ the original series contains for a given shape and scale of the original wavelet. Correlations between the wavelet coefficients at a given scale for two series can expose or reinforce relationships that were not seen in standard filtering or Fourier analysis. We wished to determine whether the ‘inversion of correlation’ that is seen in the simple windowed correlation is a robust feature of the data.

Following Reference Cornish, Bretherton and PercivalCornish and others (2006), the maximal overlap discrete wavelet transform (MODWT) was used on each dataset. For each wavelet scale, we calculated the same windowed correlation between the two sets of wavelet coefficients. We found the most meaningful correlations at wavelet scale 5, which corresponds to a scale of roughly 64cm in our data. Furthermore, at level 5, the correlation follows the same trend as our filtered data, having a positive correlation near the surface, dropping through zero to a significantly negative correlation at the bottom of the hole. Figure 4 shows windowed correlations at wavelet scales 3–6.

Fig. 4. Windowed correlation between wavelet coefficients at four different scales. Below level 4, no real pattern in correlation is seen. At levels 4–6 a pattern of decreasing correlation with depth is observed, which becomes significantly negative at levels 4 and 5. This increases our confidence in the trend of the correlation.

Reconciling depth measurement errors

Since the BOS and IGLS logging systems are independent, using different methods to measure depth, a depth calibration is needed to compare logs performed with the two systems. Since the BOS depth measurement was designed with precision rather than accuracy in mind, we assumed the IGLS depths are accurate and that the BOS depths require calibration. The two systems have different measuring systems, cables with different properties, and different pulleys. The basic form of the transform from original BOS depth z to IGLS depth z* is z* = mz. To determine m we chose two ‘landmark packets’ of features, one near the surface and one around 15 m, which were of the same shape in each log and were clearly the same features. We varied m to align the logs in the deeper region, ensuring also that they did not become misaligned in the shallow region. Our best value of m was 0.99. Figure 5 shows the two sets of features we used for this calibration.

Fig. 5. The two sets of ‘landmark packets’ used to co-register the two logs.

We might produce the correlation pattern discussed in previous subsections if density and returned brightness were actually positively correlated through the entire depth of our survey, and if some part of our depth calibration was incorrectly calculated or if one cable stretched during the experiment. If we went deep enough, or if the stretch was great enough, the correlation would become positive again. The length scale of features for which we see the strongest correlation and anticorrelation are in the order of 15–25 cm, so a differential stretch of 7–12cm or approximately 0.2–0.5% could produce this result. Both cable stretch and calibration errors would manifest themselves in a linear way; by varying the linear multiplier m we should be able to test and see whether we return to an all positive correlation with another multiplier. Figure 6 shows the result of varying the linear multiplier m by 1% on each side of our preferred value. Note that the decrease in correlation with depth appears to be a robust result. The strongest overall correlations are seen at and near our preferred value of m. Thus we believe we do not have a stretching cable or spurious calibration problem.

Fig. 6. Windowed correlations under scenarios of differing cable stretch. We span our preferred m value of 0.99 and calculate the correlations if the cable were stretching or contracting. Note that the reduction in correlation with depth is a robust feature of the data.

Density

The transformation of snow into ice takes place under at least three distinct regimes with different physical processes contributing to compaction. In regime 1 (≈ 0.3–0.55 gcm^–3, from the surface to about 15m at Summit), densification takes place primarily by grain-boundary sliding (Reference AlleyAlley, 1987). This mechanism ceases to be dominant when the relative density of snow approaches that of random close-packed spheres; that is, all of the ice grains have moved to a point where they are supported on all sides by other ice grains. In regime 2 (≈ 0.55–0.8 g cm^–3), further densification then takes place by pressure sintering, during which the contact bonds between grains thicken and the interstices between the grains become smaller (Reference Arthern, Wingham, Bohren, Barkstrom, Bohren and BeschtaArthern and Wingham, 1998). Eventually, the interstices become isolated from one another; this transition is known as ‘pore close-off’. In regime 3 (≈ 0.80.92 gcm^–3), the confining pressure is resisted by bubble pressure in the sealed air bubbles.

In snow, firn or ice, the amount of light returned to the borehole camera is dominated by the amount of scattering in the material. At visible wavelengths, absorption is minimal. To first order, scattering is determined by the cross-sectional area of scatterers. In the shallow regions we are concerned with here, the primary scatterer of photons is the interface between air and ice. When there is more airice interface surface area per unit volume, there will be more scattering.

In regime 1, densification takes place primarily by grainboundary sliding. If no changes in grain shape occur, this process will bring more scattering surface area into a unit volume as density increases, resulting in more scattering and greater returned brightness in the borehole log. In regime 2, further densification is by pressure sintering, which involves thickening the necks between grains and producing more rounded shapes. This process is partially driven by surface energy effects and destroys surface area, so as the firn gets denser in regime 2, there is less scattering surface area per unit volume, which decreases the returned brightness in the video log. The positive correlation begins to drop as the change between regimes 1 and 2 is reached (≈15 m). This implies that the same factors that influence dominant densification mechanisms (increasing grain co-ordination number, changing grain and pore geometry) are also responsible for this change in relationship between brightness and density.

Grain size and shape

Grain size and shape play an important role in scattering at visible wavelengths. At a constant density a smaller grain size results in more scattering surface area, and thus a greater backscattered intensity. Larger grain size has the opposite effect. Grain shape also has an effect on scattering surface area: a sphere is the solid shape with the lowest surface:volume ratio, so as grains become more spherical they lose scattering surface area and scattering decreases.

Several modeling studies (Bohren and Barkstrom, 1974; Reference Wiscombe and WarrenWiscombe and Warren, 1980; Reference WarrenWarren, 1982) have shown the effect of grain size in radiative transfer, so we expect that returned brightness is indicative of grain size. Two important complications prevent us from attempting a simple correlation study between grain size and returned brightness. The most important complication is that grain shape, in addition to grain size, is very important in scattering. Reference Grenfell and WarrenGrenfell and Warren (1999) showed that for any shape of snow grain, the important dimension for visible light scattering is the average path a photon takes through the grain, which, with most grain shapes, is close to the shortest path. The second most important and related complication arises from uncertainties in reporting of grain size. For example with depth-hoar ‘plate-like’ grains, the thickness of such a grain is the important dimension for scattering, whereas the diameter of the grain is likely to be reported.

Grain-size-density correlation

Bohren and Beschta (1979) noted that, since grain size and density are often covariant, it is difficult to distinguish their contributions to radiative transfer. Near the surface at Summit, high-density fine-grained winter snow alternates with low-density large-grained summer surface hoar. Since both increasing density and decreasing grain size should lead to increasing returned brightness, the correlation between density and grain size reinforces, or could even be the sole cause of, the apparent correlation between optical brightness and density. Grain size and density would need to become anticorrelated to produce the negative correlations between brightness and density we see below 20 m.

Density ‘inversion’

Reference Gerland, Oerter, Kipfstuhl, Wilhelms, Miller and MinersGerland and others (1999) noted that variations in the density of a core collected at Berkner Island, Antarctica, appeared to undergo an ‘inversion of correlation’ with electrical conductivity (ECM) measurements on the core. Above 25 m, the peaks in density were anticorrelated with peaks in ECM (interpreted as summer peaks), and were correlated below 25 m. A modeling study by Reference Li and ZwallyLi and Zwally (2002) found that initially lower-density late-spring and summer snow reached higher densities than late-fall and winter snow. Other studies in snow pits and shallow cores (e.g. Reference Shoji, Langway, Oeschger and LangwayShoji and Langway, 1989) have found the reverse to be true: higher densities correspond with winter signals in the isotope record even deeper in the core. Chemical analysis of another core from our site (personal communication from J.R. McConnell) shows that such a ‘density inversion’ does not occur at our site.