We examine a firn core from a dome in southeast Greenland that exhibits distinct firn densification. The ice was -20.9 °C at 20 m depth, and the core gives an average accumulation rate of 1.0 m w.e. yr-1 in water equivalent. However, the close-off density of 830 kg m-3 occurs at 83.4–86.8 m depth, which is about 20-m shallower than that obtained from two empirical models. Where the density ρ > 750 kg m-3, the densification appears faster than that from the empirical models. As a result, compared to the empirical coefficient, the actual compactive viscosity coefficient is nonlinear and decreases at ρ > 750 kg m-3, indicating that the firn with a higher density is softer than that from the empirical result. We argue here that the high accumulation rate creates a high overburden pressure in a short time. Thus, the relative softness of the firn may arise from (1) there being not enough time to form bonds between grains as strong as those in a lower accumulation-rate area, and similarly, (2) the dislocation density in the firn being relatively high.
Introduction
Polar ice sheets are good archives of paleoenvironmental events through the identification of proxies preserved in the ice. Such paleoenvironmental proxies are particularly well identified and dated in ice-sheet domes. Therefore, many ice cores have been drilled from ice sheet domes such as Dome Fuji (Watanabe et al., 2003), EPICA Dome C (EPICA community members, 2004), GRIP (Greenland Ice-Core Project Members, 1993), GISP2 (Grootes et al., 1993), and NGRIP (North Greenland Ice Core Project Members, 2004). Such domes often have common characteristics such as (1) a low accumulation rate, due to being in a polar inland area, and (2) a low temperature, due to being inland and at a relatively high elevation. Because the areas have low accumulation rates and low temperatures, the firn cores can provide reconstructions to past environments up to several hundred thousand years old. Moreover, as the areas experience limited melt, the measurements are of high quality. However, firn cores from areas with low accumulation rates have the disadvantages of low temporal resolution for the purpose of environmental reconstruction and might not track some seasonal or annual events (Kameda et al., 2008).
For paleoenvironmental reconstruction by gas proxy from ice cores, firn densification is an important factor. Firn densification is also a consideration for mass fluctuations of glaciers and ice sheets (Bader, 1939, 1958; Benson, 1962; Anderson and Benson, 1963), with the basic characteristics described in textbooks (e.g., Cuffey and Paterson, 2009). In inland Greenland, the transition from firn to ice typically occurs at a depth of 50 to 80 m and at ages of 100 to 300 years (e.g., Schwander et al., 1993; NEEM community members, 2013; Matoba et al., 2015). The main physical influences on firn densification are temperature, accumulation rate, and impurity levels. Concerning the impurities, impurity in firn accelerates deformation (densification) of firn, with Ca2+ (Hörhold et al., 2012) as well as Cl-, NH42+, F- (Fujita et al., 2016) being key impurities for the deformation. Concerning temperature and accumulation rate, warm temperatures speed up the transition, but rapid accumulation increases the transition depth. In polar ice sheets, the high accumulation sites tend to be warm. This is probably because warm temperatures produce much more water vapor, which generally leads to greater precipitation rates. Thus, their temperature and accumulation have counteracting effects on the transition depth.
However, a recently studied dome area in southeast Greenland has one of the highest accumulation rates in Greenland yet is relatively cold, and thus may have novel firn characteristics. In a previous drilling project, we obtained a 90-m firn core in the southeast dome of Greenland (Iizuka et al., 2016). The site (67.18°N, 36.37°W, 3170 m a.s.l.) is located 185 km north of the town of Tasiilaq in southeastern Greenland. Hereafter; we call this site “SE-Dome.” (This site is also called “Ammassalik Ice Cap” in Weidick and Morris, 1998, or it may be called “Dome Ammassalik.”) The borehole temperature at a depth of 20 m was -20.9 °C. The main Greenland ice divide has a fork at the southern Summit (GRIP/GISP2). In the southern area of the fork, the two ice divides extend southwest to near Narsarsuaq through Dye 3, and extend southeast to near Tasiilaq. Likely due to the presence of a mountain under the ice sheet (Bamber et al., 2013) and to a high snow accumulation (Burgess et al., 2010), the SE-Dome area forms a dome more than 3000 m above sea level (Fig. 1).
According to Bales et al. (2009), the region has an accumulation rate of 0.6–0.8 m in water equivalent (w.e.), which is higher than that at other Greenland domes, due to a high moisture supply from the Icelandic low in the nearby Atlantic. Also, according to analysis of the DAS2 firn core (67.5°N, 36.1°W), the annual accumulation during the years from 1936 to 2002 was about 0.9 m (Pedro et al., 2012). Thus, a firn core from the SE-Dome will have the advantages of coming from the highest accumulation dome in Greenland and be of high quality due to the cold temperatures. To obtain comprehensive knowledge for firn densification, we should clarify the firn densification mechanism under conditions of a high accumulation rate.
In this study, we analyze a firn core in the SE-Dome region that extends below the close-off depth (Iizuka et al., 2016). Here we describe the core's physical characteristics, focusing on the firn densification process of the core as a case of high accumulation rate with low temperature.
Ice Core Processing and Analytical Procedures
The SE-Dome core (Fig. 1) was drilled to 90.45 m depth during 22–27 May 2015 and then transported by a 20-ft reefer ship from Tasiilaq, Greenland, to the Institute of Low Temperature Science (ILTS) at Hokkaido University, Japan, arriving on 24 August 2015 (Iizuka et al., 2016). During transit, the ice was kept below -25 °C. Upon arrival, we first confirmed that all firn-core sections were undamaged and had high quality. Then, we processed and analyzed the ice in the ILTS laboratory cold room.
For the analyses, we run stratigraphical observations and bulk density measurements on whole sections. Bulk density is measured with a volumetric method (measuring weight and size of the cores). A continuous density profile of the SE-Dome firn core is also measured using the X-ray transmission method reported by Hori et al. (1999). In this method, the intensity of X-rays transmitted through a firn core sample is continuously measured using an X-ray detector during translation of the sample across the beam. The X-ray intensity profile is then converted into a density profile using a calibration curve for X-ray absorption based on ice thickness. The spatial resolution of the density profile is approximately 1 mm. To detect volcanic events, and thus locate dates, we run electrical-conductivity measurements via the continuous dielectric profile (DEP) method (Fujita et al., 2016). This method produces a profile of electrical conductivity at 250 MHz. To detect the year 1963, the tritium content is determined using the liquid scintillation method after distilling the meltwater (Kamiyama et al., 1989). This method has an analytical resolution of 500 mm, which corresponds to about a half year.
According to a previous study, the ion concentrations in the surface snow are lower than those at other sites in inland Greenland (Iizuka et al., 2016; Oyabu et al., 2016). The reason is probably due to a dilution effect from the high accumulation. However, the ion fluxes are nearly the same as those in the GISP2 (Summit) snow (Oyabu et al., 2016), implying that the contribution of impurity to the firn deformation is smaller than that at other sites in Greenland. So, for this study, we do not account for impurity effects on firn deformation.
FIGURE 1.
Location of SE Dome. Base of Greenland elevation map is from Helm et al. (2014). Right: close-up of study location. The core is from 67.18°N, 36.37°W, and 3170 m a.s.l.
Results and discussion
Stratigraphy and Density of Cores
The SE-Dome core consists of 189 sections, the average section length being 0.479 m. The bulk density of these sections increases with depth as plotted in Fig. 2, part a (See Table A1 for the raw values). At about the 13.8 m depth, the value 550 kg m-3 is reached, and then at about 20.2 m, the value reaches 600 kg m-3. This density indicates the point where the firn grains stop rearranging (Fujita et al., 2014). Then at about 64.0 m depth, 760 kg m-3 is reached, meaning that below this depth, dislocation creep is a significant factor until close-off (Salamatin et al., 2009). Finally, at about 86.8 m, the close-off density of 830 kg m-3 is reached. These bulk densities agree well with the X-ray density measurements. For example, the X-ray close-off density is reached at 83.4 m. In comparison to other cores, the SE-Dome core has a relatively deep and young close-off depth (Fig. 3).
The observed number of ice layers equals 60, with an average thickness of 3.6 mm (Fig. 2, part a). Most of the ice layers are <5 mm thick, but several are much larger. For example, at 19.355 m depth (summer 2006), the ice layer is about 20 mm thick, and at depths of both 22.715 m (about 2004) and 86.490 m (about 1961) lie ice layers about 15 mm thick. Also, the 7.815 m depth has 7.1-mm ice layer, which is probably due to summer melting in 2012 (Nghiem et al., 2012). There is no ice layer at all near the surface after the ice layer in 2012, indicating cool summers around this region after 2013 to present. To determine the age of these depths, we count the density maxima and minima.
The profile of the X-ray density (Fig. 2, part b) has several peaks that exceed twice the standard deviation from a 2-m running average. These peaks indicate ice layers as described above. Indeed, depths having ice layers over 5 mm thick occur where there are X-ray density peaks. The standard deviation of the 2-m running mean is about 30 kg m-3 near the surface and decreases to 5 kg m-3 at 20 to 30 m depth (580 and 650 kg m-3). In deeper firn, the standard deviation increases with depth to 15 kg m-3 at the close-off depth.
The minimum value of the standard deviation, here between 20 and 30 m (580 and 650 kg m-3), in general marks the crossover point (Hörhold et al., 2011; Fujita et al., 2014, 2016). At this point, an initially lowdensity layer overtakes that of an initially high-density layer. Concerning season variations, wind forcing in winter in inland Greenland produces a homogeneous high-density surface snow (Benson, 1962). But during summer, insolation and temperature forcing after deposition produces a mixture of high- and low-density snow. So, the initially low-density layers come from summer precipitation, the high-density layers come from winter. As a reference, in this (southeastern) region, most precipitation falls during the winter months (Cappelen et al., 2001).
FIGURE 2.
SE Dome firn-core profiles, (a) Bulk density (red squares), averaged x-ray density (blue triangles), and thickness of ice layers (purple circles). For the raw data of bulk and x-ray density, see Appendix, Table A1. (b) X-ray density (blue), and its standard deviation from the 2-m running average (green).
As the 2-m running-mean length roughly equals the annual accumulation, deviations probably reflect seasonal variation. Thus, the SE-Dome region has about 60 kg m-3 (1 σ) of seasonal density variation near the surface, which is smaller than the modeled one (about 200 kg m-3 under an accumulation rate of 0.9 m w.e. yr-1; Li and Zwally, 2004).
Accumulation Rate of SE-Dome Firn Core
The smaller-scale density changes derive from the high-resolution X-ray density profile in Figure 4. The density fluctuates down to the 20-m depth with a period of 1 to 1.5 m, indicating initial winter high- and summer low-density layers. The fluctuations disappear from 20 to 30 m at the crossover point. Below the 30 m depth, the fluctuations reappear, probably due to having inverted summer high- and winter low-density layers.
Some conductivity peaks are detected (Fig. 4). The conductivity peak at 11.745 m depth is probably due to the eruption of the Eyjafjallajökull volcano from March to June 2010. In agreement with the eruption date, the 11.745 m depth corresponds to spring 2010 from counting maxima in the X-ray density profile (Fig. 4, part a). Moreover, according to the Volcanic Ash Advisory on the MET Office UK ( http://www.metoffice.gov.uk/), volcanic materials were transported to southeastern Greenland at this time. Thus, using this date, the 11.745 m depth corresponds to 5.27 m in water equivalent, indicating an accumulation rate of 1.05 m w.e. yr-1 from spring 2010 to spring 2015.
The highest conductivity peak occurs at 43.420 m depth (Fig. 4, part b). The peak is probably due to the Pinatubo eruption on 15 June 1991. The 43.420 m depth corresponds to late autumn because the inverted density profiles correspond to a decreasing trend just before a minimum (Fig. 4, part b). This several-month time lag is likely due to the long distance for the eruption products to travel (Soden et al., 2002). The 43.420 m depth corresponds to 24.89 m in water equivalent, indicating an accumulation rate of 1.04 m w.e. yr-1 from autumn 1991 to spring 2015, and 1.08 m w.e. yr-1 from autumn 1992 to spring 2015..
Another fixed date is provided by the tritium profile in Fig. 4, part c. The tritium peak at 81.375–81.875 m depth corresponds to 1963, arising from fallout from hydrogen-bomb tests. The depth corresponds to 52.98–53.38 m in water equivalent, indicating an accumulation rate of 1.02–1.03 m w.e. yr-1 from 1963 to spring 2015.
These three comparisons between 1991 and 1963 indicate that the high-resolution X-ray density profile in Figure 4 preserves annual fluctuations. But due to the low-amplitude of the fluctuations near the crossover depth, this annual counting is not perfect. Nevertheless, the high accumulation rate may enable partial annual counting below the cross-over depth. Such counting indicates that the ice close-off occurs in 1962, meaning that 53 years is needed to close off.
In summary, the SE-Dome firn core has an accumulation rate of about 1.0 (1.02 to 1.08) m w.e. yr-1 with little decadal fluctuation. In the following discussion, the firn temperature and accumulation rate of the SE-Dome core are fixed at —20.9 °C and 1.0 m w.e. yr-1.
Comparison with Firn Densification Model
Many physical-based models of firn densification have been proposed (e.g., Arthern and Wingham, 1998; Zwally and Li, 2002; Helsen et al., 2008; Salamatin et al., 2009); however, most require many physical parameters, and some do not match measured profiles (Cuffey and Paterson, 2009). Thus, instead we use empirical fittings. For the polar high-elevation area, Sorge's Law (Sorge, 1935; Schytt, 1958) as well as Herron and Langway's model (Herron and Langway, 1980) are such fittings that match well with measured profiles of steady-state densification (Cuffey and Paterson, 2009). Fitting to Sorge's Law requires only the surface density (ρs), here 300 to 400 kg m-3, and the close-off depth (hc). The density (ρh) at any depth (h) is
FIGURE 3.
Characteristics of several firn cores with a range of temperatures and accumulation rates. (a) Relation of ice temperature with close-off depth. (b) Close-off age of ice. (c) Accumulation rate. For the raw data, see Table A2 in the Appendix.
As shown in Figure 5 (parts a–c), the depth-density curves derived from the parameter (hc/1.9) match well with measured profiles in some regions in the polar high-elevation area. However, such a match does not occur with the SE-Dome firn core. Figure 6 shows several attempts to match this core to Sorge's Law. For both surface densities, the curves do not fit with the parameter (hc/1.9 = 44.7 in the case hc = 85 m). Instead, the hc = 70% curve fits at ρ < 550 kg m-3, and the hc = 130% curve fits at 600 < ρ < 750 kg m-3. At ρ < 550 kg m-3, the discrepancy may be related to the use of constant values of the surface density, with the DF and NEEM cores in Figure 5 showing a similar trend. However, unlike those other cores, at 600 < ρ < 750 kg m-3, the data do not fit with the hc = 100% curve, instead fitting hc = 130%. The 130% higher fitting suggests that the close-off depth should be about 108 m instead of the actual depth of 83.4–86.8 m.
Such a fit is similar to that found for the firn core drilled at Mount Wrangell, Alaska (Shiraiwa et al., 2004), a glacier with a high accumulation rate. That is, the depth-density curve of the Wrangell firn core shown in Fig. 5, part e, fits best when the parameter is 130% higher than hc/1.9. Both of these cores densify faster than Sorge's Law at densities ρ > 750 kg m-3. In comparison, consider the ice from Mount Belukha, Russian Altai (Fig. 5, part d), which is mountain glacier in a high-elevation area with a normal accumulation rate. The depth-density curve of the Belukha firn core fits well with the parameter hc/1.9 (here 19.47 m). The features common to both SE-Dome and Wrangell are their high accumulation rates (1.03 and 2.49 m w.e. yr-1 w.e.) and younger close-off age (Fig. 3).
The depth-density curve does not match Herron and Langway's model well either. For the initial stage of densification (ρ < 0.55 kg m-3), the density (ρh) at depth h is
FIGURE 4.
High-resolution x-ray density profile (blue), electrical conductivity (orange), and tritium concentrations (brown) of the SE Dome firn core. The density profile is a 40-mm running mean. The point marked A is the peak from the Eyjafjallajökull volcano on March to June 2010; B is the peak from the Pinatubo eruption on June 1991; C is the peak from nuclear tests in 1963.
where
Here k0 = 0.0862 at-20.9 °C.
For the following stage of densification (ρ > 0.55 kg m-3), the density (ρh) at depth h is:
where
Here k1 = 0.0211 at -20.9 °C, and the accumulation rate A = 1.0 m w.e. year-1.
Figure 7 compares the measured profile to model results. At the initial stage of densification, when ρ < 0.55 kg m-3, the depth-density curve matches the model's result for 0.36 kg m-3 of surface density. But at the following stage of densification, when ρ > 0.55 kg m-3, the depth-density curve of the SE-Dome firn core does not match the model's result for 1 m w.e. yr-1 of annual accumulation. For this accumulation rate, the estimated close-off depth would be about 107–108 m in depth, the same value predicted from Sorge's Law and much deeper than the actual depth (from 83 to 86 m).
Firn Densification Mechanism in a High Accumulation Area
We consider here why the depth-density curve of SE-Dome firn core did not agree with the empirical models. In particular, we ask why the SE-Dome core densified faster at ρ > 750 kg m-3 than that predicted by Sorge's Law (Fig. 6). Figure 6 shows a good fit first to the Hc = 70% curve at ρ < 550 kg m-3 and then to the Hc = 130% curve at 600 < ρ < 750 kg m-3. But then the measured density increases faster than the 130% curve at ρ > 750 kg m-3. Consider the compactive viscosity coefficient (ηc; Pa s-1) in Figure 8, part a. The coefficient of the actual density profile is calculated from the equation
FIGURE 5.
Comparison between measured density-depth profiles (red lines) with fits based on Sorge's Law. (a) Dome Fuji (Hondoh et al., 1999), (b) NEEM (Fujita et al., 2014), (c) SIGMA D (Matoba et al., 2015), (d) Belukha (Takeuchi et al., 2004), and (e) Wrangell (Shiraiwa et al., 2004). Light green curve is the fit using the parameter hc/1.9. Green and yellow curves are those using the parameter 1.3 times larger (130%) and 0.7 times larger (70%), respectively. The close-off depths hc are listed in Appendix Table A2.
where, ρ, σ, and t are density (kg m-3), overburden pressure (Pa), and time (s), respectively. On the other hand, the empirical compactive viscosity coefficient (η) with density dependence is calculated from the equation (Nishimura et al., 1983)
FIGURE 6.
Same as Figure 5, but for the SE Dome firn core. Density-depth profiles are bulk (red) and x-ray (blue) measurements. (a) With initial density of 360 kg m-3. (b) Initial density of 390 kg m-3.
where, η0 = 0.001 to 0.007 N*s m-2, K = 2.57 × 10-3 m3 kg-1, ΔE is an activation energy equal to 51.6 kJ mol-1, kb is Boltzmann's constant, and T is the temperature. The empirical plot in density versus compactive viscosity coefficient in Figure 8, part a, shows a wide range of values because of a wide range of values for η0. As a result, direct comparison is not possible between the empirical and the actual coefficients. However, the fit is linear in the linear-log plot at the lower densities. On the other hand, the actual compactive viscosity coefficient (ηc) is nonlinear (Fig. 8, part a), saturating at a fixed value when ρ >750 kg m-3. The lower compactive viscosity coefficient at ρ > 750 kg m-3 means that the SE-Dome firn at p > 750 kg m-3 is actually softer than the empirical relation predicts. This indicates that the SE-Dome firn is more deformable at ρ > 750 kg m-3.
FIGURE 7.
Same as Figure 6, but instead compared with the Herron and Langway (1980) model. Measured density-depth profiles are bulk (red line) and x-ray (blue) measurements. At the initial stage of the densification (ρ < 550 kg m-3), black, dark gray, and light gray curves are model results for surface densities of 0.39, 0.36, and 0.30, respectively. In this model, the results are sensitive to accumulation rate only when ρ > 550 kg m-3. Orange, yellow, light green, green, and light blue curves are model results for accumulation rates of 0.5, 0.75, 1.0, 1.25, and 1.5 m w.e. yr-1, respectively. Model parameters are K0 = 0.0862 and K1 = 0.0211, with a temperature of -20.9 °C. Parameter h0.55 is set to our measured value of 13.8 m.
To better understand the densification, consider the relation of overburden pressure (Pa) to strain rate (m yr-1). Comparing various sites, the SE-Dome core has a higher strain rate than other Greenland sites (SIGMA-D and NEEM cores) at a given overburden pressure (Fig. 8, part b). The difference is especially large, about one order of magnitude, at higher pressures (> 4 × 105 Pa; 750 kg m-3). This indicates SE-Dome firn is more deformable at ρ >750 kg m-3 compared to that at other Greenland sites. The Wrangell core has an even higher strain rate than the SE-Dome core. As the Wrangell core has about 2.5 times the accumulation rate of the SE-Dome core, the Wrangell firn may be more deformable than SE-Dome firn. On the other hand, Belukha firn is less deformable than SE-Dome firn. Of the five cores plotted in Fig. 8, part b, Belukha firn has the highest ice temperature, indicating that this relation of overburden pressure (Pa) and strain rate (m yr-1) does not depend on the ice temperature. Rather, accumulation rate is one of the key factors that determines the strain rate for a given overburden pressure.
FIGURE 8.
Inferred ice properties from the core, (a) Compactive viscosity coefficients (Pa s-1). Blue and red circles are coefficients of bulk density from Equation (1) in the text. Blue circles are calculated from raw data. Red circles are calculated from a sixth-order polynomial approximation of the density-depth plot. As the raw data produces some negative coefficients because of density reversion between adjacent datapoints, the polynomial approximation is also used for the calculation. For the constants in the polynomial approximation, see Appendix, Table A3. Light green (η0 = 0.001) and blue lines (η0 = 0.005) are empirical coefficients from Equation (2) in the text, (b) The relation between overburden pressure (Pa) and strain rate (m yr-1) of several firn cores; SE Dome (red), NEEM (green), SIGMA D (orange), Belukha (purple), and Wrangell (light blue). Polynomial approximation of the density profiles is used for the calculation. For the constant numbers of polynomial approximation, see Appendix, Table A3.
We have two possible reasons why the SE-Dome firn is more deformable at ρ > 750 kg m3 than prediction. First, the SE-Dome region has one of the highest accumulation rate areas in polar ice domes (Fig. 3). A high accumulation rate creates a high overburden pressure in a short time. The short time leads to a weaker bond strength between grains than that of the same depth in a lower accumulation rate area. This condition makes it easier to deform (densify) the snow/firn than that of the same depth in a lower (or normal) accumulation rate area. In other words, firn in high accumulation rate areas are predisposed toward a high overburden pressure at ρ > 750 kg m-3 without fully bonded growth, resulting in a more rapid densification than that in the empirical steady-state condition. The second possible reason is that, dislocation creep is a significant process in densification at ρ > 750 kg m-3 (Salamatin et al., 2009). As a high accumulation rate creates a high overload pressure in a short time, the dislocation density is likely to increase in firn in a shorter time than that in firn with a normal accumulation rate. Thus, the SE-Dome core may have faster densification at ρ > 750 kg m-3 than the depth-density curve with a normal accumulation rate.
Conclusion
We have shown that the core from SE-Dome in Greenland has a distinct firn-densification profile due to the area's high accumulation rate. Probably because of the high accumulation rate, the SE-Dome firn core preserved its annual fluctuation even after the cross-over point and caused the depth-density curve to deviate from Sorge's Law and the Herron and Langway model. Concerning the latter, the modeled close-off depth (108 m) is over 20 m deeper than the actual depth (from 83.4 to 86.8 m).
The actual compactive viscosity coefficient was nonlinear, particularly at ρ > 750 kg m-3, indicating that the SE-Dome firn at ρ > 750 kg m-3 is softer than that from empirical plots. Among firn cores from other areas, both of the high-accumulation cores (SE-Dome and Wrangell) tend to be more deformable (high strain rate) at the same overburden pressure than that from the models. We offered two hypotheses for this greater deformability at ρ > 750 kg m-3. The high accumulation rate creates a high overburden pressure in a short time. The short timing has two effects: Compared to firn in a lower accumulation-rate area, here (1) there is not enough time to form strong bonds between grains, and (2) the dislocation density is likely to be higher.
Acknowledgments
We are grateful to the drilling team of SE-Dome ice. The paper was significantly improved as a result of comments by two anonymous referees and the handling by Scientific Editor Dr. A. Jennings, to whom we are greatly indebted. This study was supported by MEXT/JSPS KAKENHI Grant Number 26257201 and 16K12573, Joint Research Program of the Institute of Low Temperature Science, Hokkaido University, and the Readership program of the Institute of Low Temperature Science, Hokkaido University. The analysis of tritium concentration was supported by National Institute of Polar Research through General Collaboration Project no. 27–13. This study is partly responsible for ArCS (Arctic Challenge for Sustainability Project; PI Shin Sugiyama)
References Cited
Appendices
Appendix
TABLE A2
Temperature, accumulation rate, close-off depth, and age of several firn cores.
TABLE A3
Parameters (A–G) of the sixth-order polynomial approximation in Figure 8. For Dp (depth [m]) and Dn (density [kg m -3]), Dn — A Dp6 + B Dp5 + C Dp4
