2.1 Field-site measurements

During the cruise ANT VIII/5 of RV Polarstern in 1989–90, a core was recovered from a hole drilled mechanically to a depth of 215 m in the Ronne Ice Shelf at 76°58’s 52° 16′ W, located 30 km away from the ice-shelf front (site Β13, Fig. 1). The location was chosen based on earlier electromagnetic reflection (EMR) profiling by a group from the University of Münster which indicated the ice was laterally homogeneous in the vicinity and upstream of the site (Reference Blindow and MillerBlindow, 1990). Based on the EMR data, the ice thickness was determined as about 240 m with a marked discontinuity at roughly 155 m (Reference Blindow and MillerBlindow, 1990). The site was located within the peripheral ice-shelf zone with vigorous bottom ablation.

Drilling was conducted with a mechanical rig providing a core of approximately 72 mm diameter. Core processing at the site comprised stratigraphie description and photodocumentation, continuous measurements of d.c. conductivity and density measurements by weighing cylindrical sections (Reference OerterOerter and others, 1992). A temperature log was obtained over a period of 2d, 3 weeks after the start of drilling, by allowing a thermistor sensor to attain thermal equilibrium at positions spaced a few metres apart.

2.2 Laboratory measurements

Apart from the visual core stratigraphy, 31 horizontal thin sections at approximately 10 m intervals have been prepared (plus eight at close spacing and a further 15 vertical sections). For these sections, crystallographic c-axis orientations have been determined with a universal stage. The thin sections have also been recorded with a video camera for an evaluation of grain-size and shape, employing image-processing techniques as described by Reference EickenEicken (1993). In brief, two images (50 mm wide) of a thin section placed between crossed polarizers at different, pre-defined orientations are digitized. With the aid of non-linear filtering routines, signals resulting from pores are removed from the images. After union of the two frames, a Sobel filter which enhances regions of high spatial contrast is applied. Following binarization about a threshold value, the image is segmented into grains and grain boundaries to determine size and distribution of grains. For comparison with manual measurements (e.g. Reference GowGow, 1969; Reference Lipenkov, Barkov, Duval and PimientaLipenkov and others, 1989), the average cross-sectional area, A_mean, has been determined by counting the number of grains cut in individual thin sections of a known area. For the four upper thin sections taken within the firn layer, where pores account for a significant part of the thin section, A_mean has been corrected based on the firn density at the respective depth.

Electrolytical conductivities have been determined on melted cuttings over the entire length of the core, with values integrated over approximately 0.8 m depth for each core segment. Measurements were taken with a WTWLF191 conductivity probe at temperatures between 10° and 20°C with conductivities corrected to a reference temperature of 25°C. Concentrations of major ions, ²H and ¹⁸O h ave been determined at selected depth levels (Reference OerterOerter and others, 1992).

3.1 General stratigraphy

The upper 150 m of the core displays the typical sequence of snow grading into firn with a transition to bubbly ice at depth. Below an undulating discontinuity extending over 10–20 mm depth at 152.8 m, the core takes on a completely different appearance. The ice is transparent due to the lack of gas-filled pores. At depths between 152.8 m to approximately 159 m numerous spherical aggregates (few millimetres diameter) of particulate inclusions (mostly clay and silt size fractions (personal communication from R. Petschick, 1992)) occur in strings or layers with few centimetres vertical separation throughout the ice. Below 159 m these aggregations decrease in number. Closer inspection of the ice reveals a faintly visible network of liquid inclusions, mostly confined to grain boundaries and triple-grain junctions. Scanning electron microscope (SEM) analysis of samples from four depths also demonstrates the intergranular distribution of salts within the ice (Reference Moore, Reid and KipfstuhlMoore and others, 1994). As proposed in previous studies (Reference Engelhardt and DetermannEngelhardt and Determann, 1987; Reference ThyssenThyssen, 1988) and according to stable-isotope measurements (Reference OerterOerter and others, 1992) as well as other evidence discussed below, the discontinuity marks the transition from meteoric ice deposited as snow at the upper surface to marine ice accreted from below.

3.2 Density profile of firn and ice

The depth–density profile of the core appears linear from 10 to 60 m depth ( Fig. 2a). Below that, the curve asymptotically approaches the maximum theoretical density of ice. The scatter below 75 m depth is due to the poorer quality of the core segments rather than representing true variability. From the core stratigraphy, it appears that the inflection in the profile at 37 m depth is due to a combination of decreasing core quality and the appearance of ice lenses. The maximum density attainable through physical re-arrangement of grains (c. 550 kgm⁻³; Reference PatersonPaterson, 1981, p. 10) is surpassed at a depth of approximately 12 m. The transition from firn to ice, as defined by pore close-off density of 830 kgm⁻³, occurs at roughly 50 m depth. For accumulation rates varying between 204 and 154 kg m⁻²a⁻¹ and 10 m temperatures

Fig. 2.a. Depth-density profile of the upper 100 m of the cort. Solid line is an eighth-order polynomial fit to the data. b. Densification rate vs density of ice and firn at B13 based on the computed age–depth function (solid line). Dashed and stippled lines from Reference Alley and BentleyAlley and Bentley (1988) as measured at sites BC and UpB on the Siple Coast, Antarctica. The bars mark the positions of the 10 m (simple bar), 25m (top cross-bar) and 50m (top and bottom cross-bar) depth levels. Dots computed from Greenland data given by Reference GowGow (1968).

Based on the ice-shelf dynamics data gathered in the framework of the Filchner-Ronne Ice Shelf Programme (FRISP), we can assess the density–age relationship and potential strain-rate effects on densification through application of a simple ice-shelf flow model (Reference ThomasThomas, 1973; for details see section 4.1). The model compares quite well with the ¹⁸O and ²H record for this and other shallow drill sites in the vicinity (Reference Graf, Miller and OerterGraf and others, 1991). As shown in Figure 2b, the densification rate derived from the computed age–depth relation decreases in a near-linear fashion at densities between 500 and 900 kg m⁻³. At the righthand end of the curve, ice layers are approximately 300 years old and have experienced roughly 40% vertical compressive strain. In comparison, data from Reference Alley and BentleyAlley and Bentley (1988) collected at two sites (UpB and BC) on the Siple Coast in Antarctica, with accumulation rates of 79 and 82 kg m⁻²a⁻¹ and 10 m temperatures of −26.4° and −26.5°C are in the same range or below the B13 data. The discrepancy between BC and B13 values is most likely due to lower 10 m temperatures and accumulation rates at the Siple Coast sites, whereas the UpB densification rates are thought to be anomalously high due to the softening effect of large deviatoric stresses in the ice stream (Reference Alley and BentleyAlley and Bentley, 1988). The dependence of dp/dt on accumulation rate should also explain the factor 1.5–2 difference in densification rates between B13 and sites in Greenland (Reference GowGow, 1968) with values of 400kg m⁻² a⁻¹ (site 2) and 340kg m⁻²a⁻¹ (Camp Century), yet similar temperatures (−24°C). Also, taking into account the slight temperature increase with depth at site B13 (−21°C at 50 m depth), it appears from Figure 2b that densification rates in the Ronne Ice Shelf with vertical strain rates of 1 × 10⁻³ to 2 × 10⁻³ a⁻¹ are not enhanced as compared to Siple Coast and Greenland sites.

3.3 Thin-section studies of core texture and fabric

Horizontal and vertical thin sections have been prepared at regular depth intervals excepting the top 38 m of firn. With the aid of automated image-analysis techniques (for details see Eicken, 1993), the grain-boundary density Β _A has been determined as a key tcxtural parameter. Β _A is defined as the length of grain boundaries per unit area. It can be of use in describing the gradual minimization of free boundary energy as a driving force for grain growth. Generally, Β _A scales inversely with mean grain-size, assuming grains of convex outlines. The depth profile of Β _A is shown in Figure 3. The grain-boundary density decreases by a factor of 3 with depth within the meteoric ice layer (thin-section photographs in Figures 4a and 5a). Intragranular pores (distinct in Figure 5a) appear at a depth below approximately 58 m, i.e. close to the firn-ice transition. At depths below roughly 95 m, grains of meteoric ice deviate from the fully convex, isometric shape. Furthermore, crystals begin to exhibit wavy extinction and polygonization.

Fig. 3. Profile of grain-boundary density Βb^A with depth as determined on thin sections employing automated image-analysis techniques (closed circles). Also shown is the mean cross-sectional area of grains as determined manually (crosses). Open circles mark layers of roughly equal cumulative strain (see section 4.3).

Fig. 4.a. Photograph of a horizontal thin section of meteoric ice at 38.44 m depth taken between crossed polarizers (mm scale at the side). Pores faintly visible as black dots at grain junctions, b. c-axis fabric diagram (Schmidt-net plot) of the sample shown in Figure 4a (98 crystals measured).

Fig. 5.a. Photograph of a horizontal thin section of meteoric ice at 136.95 m depth taken between crossed polarizers (mm scale at the side). Pores visible within grains, b. c-axis fabric diagram (Schmidt-net plot) of the sample shown in Figure 5a (55 crystals measured), c. Size distribution of cross-sectional feature or grain areas of the thin section shown in Figure 5a, as determined through morphological filtering.

For comparison, Figure 3 also shows the depth distribution of mean grain cross-sections, A_mean, determined manually. The meteoric ice layer is characterized by a linear increase of grain-size down to 120 m depth in concordance with observations from ice-sheet cores (Reference GowGow, 1969). The grain-sizes reported by Gow range below the values reported here due to the different thermal histories of the ice. Similar grain-sizes have been observed in the Amery Ice Shelf (Reference WakahamaWakahama, 1974) and the Ross Ice Shelf (Reference GowGow, 1963). In fact, the Amery Ice Shelf core is similar to BÍ3 in many ways regarding texture and c-axis fabric, as well as the distribution of liquid and solid impurities. The variability in-A_mean compared to grain-boundary density is mainly due to the appearance of large grains with indented outlines (Figs 5a and 7a).

Fig. 7.a. Photograph of a horizontal thin section of marine ice at 206.64 m depth taken between crossed polarizers (mm scale at the side). b. c-axis fabric diagram (Schmidt-net plot) of the sample shown in Figure 7a (43 crystals measured).

The discontinuity between meteoric and marine ice is accompanied by a marked increase in grain-boundary density Β _A by a factor of c. 2.5 ( Fig. 3), corresponding to a sharp decrease in grain-size with A_mean decreasing by a factor of 6. At greater depths, Β _A decreases to values typical of the lower sections of the meteoric ice layer and A _mean increases again. An examination of vertical thin sections reveals that in the vicinity of the meteoric/ marine-ice discontinuity, grains are commonly arranged into horizontal rows (see also figures shown in Reference OerterOerter and others (1992)). At the top of the marine ice, most grains are elongated by a factor of 2–5 in the horizontal direction. At greater depths, this elongation is less distinct or absent; neither is it detectable in the meteoric ice above the transition. Close inspection shows that the strings and sheets of particulate inclusions occurring mostly at depths of 152.8–159 m are commonly, though not exclusively, concentrated at grain boundaries and triple junctions.

Figures 5c and 6c provide information on the size distribution of cross-sectional grain areas, obtained through the application of non-linear, morphological filtering techniques (Reference EickenEicken, 1993). In brief, this operation can be regarded as a digital sieve, yielding the areal fraction of differently sized grains or grain protrusions. In comparing the two distributions, we note the prevalance of small features or grains in the marine-ice sample, with 55.6% of the sampled area occupied by features smaller than 2 mm and 19.0% smaller than 1 mm. The meteoric ice, on the contrary, is characterized by the dominance of larger grains, with only 14.2% of the area occupied by features smaller than 2 mm and 3.9% smaller than 1 mm.

Fig. 6.a. Photograph of a horizontal thin section of marine ice at 153.76 m depth taken between crossed polarizers (mm scale at the side).b. c-axis fabric diagram (Schmidt-net plot) of the sample shown in Figure 6a (100 crystals measured). c. Size distribution of cross-sectional feature or grain areas of the thin section shown in Figure 6a, as determined through morphological filtering.

Both methodical and sampling errors involved in the automated measurements were assessed through replicate measurements on selected thin sections and comparisons with manual measurements were made on thin-section photographs. Thus, methodical errors are estimated at less than ± 5% for B _A larger than 1.5 mm⁻, and less than ± 10% for B _A smaller than 1.5 mm⁻¹ (for a more detailed discussion of errors, see Reference EickenEicken (1993)). Spatial variability of textural parameters on a small scale may pose much more of a problem. Thus, analysis of eight horizontal thin sections spaced roughly 10 mm apart vertically varied by as much as 25% in grain-boundary density. Clearly, the issue of vertical and lateral fluctuations in grain-size and fabric should be studied in more detail. However, the general trends studied here are not strongly affected by these small-scale processes.

At the top of the meteoric ice layer and in the firn, c axes of ice crystals are distributed randomly ( Fig. 4b). Further down in the meteoric and marine ice, distributions exhibit flattening into a vertical plane (Figs 5–7b). These distributions can be understood as a result of c-axis rotation through basal glide for ice under tension (Reference AlleyAlley, 1988; Reference Lipenkov, Barkov, Duval and PimientaLipenkov and others, 1989). The c-axis distributions encountered deeper in the core are most likely a result of the Ronne Ice Shelf s stress state with extension along and little to no compression normal to the flowline, shown by geodetic strain measurements (Reference Ritter and KarstenRitter and Karsten, 1991). Similar to the clustering of c axes in a vertical plane observed by Reference Lipenkov, Barkov, Duval and PimientaLipenkov and others (1989) in the Vostok core and Reference Fujita, Nakawo and MaeFujita and others (1987) at Mizuho, c axes rotate away from the tensional axis (here roughly parallel to the flowline). The pole-figure clusters observed deeper in the ice (e.g. Fig. 5b) can in part be explained by sub-parallel alignment of adjacent grains which becomes more pronounced in older ice. Measurements of the crystal-optical misorientation between adjacent grains show that, in the topmost sample ( Fig. 4), 25% of all misorientation angles measured range below 40° with a median of 61° (N = 142), whereas at 136.95 m ( Fig. 5) 41% fell below 40° with a median of 478 (N = 129). In part, clustering may also be due to statistical under-sampling in cases where grains become large compared to sample dimensions.

For a single crystal, the shear stress resolved along the basal plane of a crystal is proportional to the geometric or Schmidt factor S = cos θ sin θ for an angle θ between the tensional axis and the crystal’s c axis. For a polycrystalline aggregate, the average geometric factor is

Field data and model results show that S_av decreases with increasing strain (Reference Fujita, Nakawo and MaeFujita and others, 1987; Reference AlleyAlley, 1988; Reference Lipenkov, Barkov, Duval and PimientaLipenkov and others, 1989). For comparison, we have computed S_av by aligning the samples with the long axis of the pole figures (determined through computation of eigenvectors of the distribution) normal to the tensional axis, thus yielding θ. The average geometric factor is plotted against the age jointly with the cumulative vertical strain for the meteoric ice in Figure 8. Age and strain have been obtained from a simple particle-path model outlined further in section 4.1. The general decrease in S_av as strain and age increase is clearly evident, corresponding to the observations of Reference Fujita, Nakawo and MaeFujita and others (1987) and Reference Lipenkov, Barkov, Duval and PimientaLipenkov and others (1989). Compared to Β13, this decrease with strain is accomplished at a similar rate in the Vostok core and at a slightly higher rate in the Mizuho core. Grain-sizes, however, are near-constant from 150 to 700 m depth at Mizuho, in contrast to the distinct increase observed in the Ronne Ice Shelf and at Vostok.

Fig. 8. Geometric factor S _av and grain-boundary density B_A of meteoric ice plotted vs age in years. Asterisks represent average geometric (Schmidt) factors of the c-axis distributions. Vertical dashed lines indicate the corresponding cumulative vertical strain (Δz/z ₀, dashed curve). Dots represent automatically measured grain-boundary densities, crosses are converted manual measurements of grain area. The drawn-out line represents the result of a particle-path simulation, assuming grain growth according to an Arrhenius-type relationship (see sections 4.1 and 4.2 for details).

3.4 Electrolytical conductivity of the melted core and brine volumes in the marine-ice layer

The results of the electrolytical conductivity measurements are shown in Figure 9. The most distinct feature of the distribution is the sharp transition from meteoric to marine ice with a corresponding increase in conductivity by almost two orders of magnitude. The mean conductivity integrated over the entire depth of the meteoric ice layer amounts to 4.8 × 10⁻⁶ S cm⁻¹ (58.3% standard deviation, as computed for individual, non-integrated measurements), while that of the marine ice with 51.0 × 10⁻¹S cm⁻¹ (45.2% standard deviation) is higher by one order of magnitude. Under the assumption that Na⁺ and CP⁻ are the major ions contributing to electrolytical conductivities, these conductivities corres-pond to salinities of roughly 0.002% and 0.026%, respectively, based on a conversion according to the compilation by Reference FreierFreier (1974) and verified by comparison with ionic concentrations reported by Reference OerterOerter and others (1992).

Fig. 9. Depth profile of electrolytical conductivity of melted core sections. Also shown is the temperature profile measured in the drill hole and the brine volume computed from these data according to the equations of Reference Cox and WeeksCox and Weeks (1983).

Data on salinity, thickness and age of marine-ice occurrences in other locations are listed in Table (1). In contrast to old marine ice found in the Ross Sea sector of the Antarctic (locations 3, 4 and 5 in Table (1)) and the Arctic (location 6), the Ronne and Amery Ice Shelves exhibit much lower salinities despite comparable ages. This contrast is stronger than suggested by the low minimum salinities shown for locations 3, 5 and 6 in Table t. In the Hell’s Gate Ice Shelf (Antarctica), the small minimum salinities are due to freezing of low-salinity meltwater (Reference SouchezSouchez and others, 1991). In the Ward Hunt Ice Shelf and the Koettlitz Ice Tongue, very few samples show salinities below l%, attributed to meltwater flushing in the latter case (Reference Gow and EpsteinGow and Epstein, 1972). Despite their age, these marine-ice layers do not differ significantly in salinity from multi-year sea ice. Salinities of the Amery and Ronne Ice Shelf cores are lower than sea ice by a factor of 20–50, with strong resemblance between vertical profiles in the two cores. Both display a sharp increase in electrolytical conductivity at the top of the marine-ice layer, with decreasing values below (Reference MorganMorgan, 1972). These close similarities extend to the microstructure and the distribution of particulate impurities.

Table 1. Approximate salinity, thickness and age of marine-ice layers and multi-year sea ice

Temperatures within the marine-ice layer ( Fig. 9) are well above the eutectic point of sea water. The fractional volume of brine V _B/V can be computed according to the equations formulated by Reference Cox and WeeksCox and Weeks (1983)

where ρ_i is the density of pure ice, S _i is the ice salinity in %o and F ₁(T) and F ₂(T) are two temperature-dependent constants derived from the phase relations (Reference AssurAssur, 1960). These relations have been specified for systems at atmospheric pressure; here, we are considering ice at water depths of approximately 150-200 m. Correcting for the sea-water freezing-point depression, however, does not increase V _B/V by more than about 1% and has consequently been disregarded. Based on stratigraphie analysis of the core and measured densities, the gas volume within the marine ice has been assumed to be zero in this case. Conversion of electrolytical conductivity measurements (Reference FreierFreier, 1974) may result in a systematic error, because these are based on NaCl being the only salt present in the solution. However, this error ranges far below the accuracy desired for the brine-volume assessment. The computed brine-volume distribution exhibits the same pattern as the electrolytical conductivity ( Fig. 9). Due to higher temperatures at the bottom, a slight increase can be observed with depth. Most of the values fall within the fractional volume range of 0.09-0.2%. This compares well with an estimate of 0.15%o made by Reference Moore, Reid and KipfstuhlMoore and others (1994) based on SEM analysis of a sample from the very top of the marine-ice layer. If the salt content were to remain constant with depth, the fractional brine volume would increase to approximately 1% at the bottom of the ice shelf.

The brine salinity S _B within the ice can be also computed from the phase relations. Thus, near the bottom of the core with temperatures around −9°C, S _B is approximately 150% but at the top of the marine layer S _B amounts to roughly 200%. With these data at hand, we can compute the volume fraction of solid salts Vss/V, i.e. NaSO₄.10H₂O and CaCO₃.6H₂O (Reference AssurAssur, 1960), according to Reference Cox and WeeksCox and Weeks (1983)

with C(T) a temperature-dependent function, the density of solid salts ρ_ss assumed as 1500 kg m⁻³ and the density of brine pB approximated as

Hence, the maximum relative volume of solid salts will be on the order of 0.01% at the top of the marine-ice layer (also depending to a small degree on the combined effects of hydrostatic pressure and temperature, which have been assumed to affect V _ss in the same way as the freezing-point temperature and S _B).

3.5 Distribution of sediment layers within the marine ice

Characteristically, the marine-ice layer contained abundant sediment inclusions, with maximum concentrations at depths between 152.8 and 159 m. Detailed analysis of these inclusions shows the millimetre-sized pellets are aggregates of clay-and silt-fraction minerals and biogenic material (personal communication from R. Petschick, 1992). The inclusions are arranged into horizontal strings and layers ( Fig. 10a). Sediment inclusions have also been reported from a core from the Amery Ice Shelf which has also been shown to be similar to the B13 core in many other respects (Reference WakahamaWakahama, 1974). In order to obtain quantitative information on the spacing and width of these features, entire core sections of roughly 0.5 m length were recorded in transmitted light with the video system used for thin-section analysis. Subsequently, images were processed in such a way as to integrate the grey-value signals within horizontal layers, assigning layers devoid of inclusions a relative optical concentration of 0 and the layer with absolute maximum impurity content a value of 1 (with a layer thickness of 0.3 and 1.2 mm depending on the chosen resolution; Fig. 10a). This allowed identification of horizons containing different amounts of particulate inclusions as shown for a 0.1 m section in Figure 10b. Whereas bulk concentrations of sediment within the ice are of the order of hundredths of grams per litre (personal communication from R. Petschick, 1992), peak values within such layers of 2–3 mm width are much higher

Fig. 10.a. Photograph of a vertical section of the core between 154.0 and 154.1 m depth (plain transmitted light), b. Relative concentration of microparticles based on integration of layer grey values over a depth range of 0.1m (corresponding to the photograph shown in Figure 10a).

Comparison of thin sections placed between crossed polarizers and in plain transmitted light confirms that inclusions are mostly confined to grain boundaries and triple junctions. Figure 10b also indicates that the sediment layers do not occur at a consistent spacing or width. This has been verified by computing the autocorrelation function (acf) for the depth series of grey values recorded both at low and high resolution (layers of 1.2 and 0.3 mm width, respectively). None of the computed aefs provided any evidence of periodicity in the data. The correlation lengths, determined from the high-resolution images, amounted to a few millimetres at maximum (1.5 mm for the sample shown in Figure 10b).

4.1 Assessing the temperature—strain history of ice sampled at site B13

The temperature and strain history of individual ice layers sampled in the core has been inferred from a particle-path model described by Reference ThomasThomas (1973). Here, the horizontal velocity of individual ice parcels is given by the ice-shelf velocity v(x), while the vertical velocity component is determined by the accumulation rate a at the ice surface and the vertical strain rate dε_z/dt. Temperatures within the ice shelf at different locations upstream of the drilling site have been linearly interpolated between the 10 m depth temperatures measured by Kipfstuhl and Oerter (1991; roughly −25^DC) and −2°C at the ice-shelf bottom. Horizontal velocity components and vertical strain rates have been obtained from the measurements of Reference Ritter and KarstenRitter and Karsten (1991) and Reference Morris, Vaughan, Miller and OerterMorris and Vaughan (1991), as well as from numerical model simulations by Determann (1991). Accumulation rates have been inferred from pit measurements (Reference Graf, Miller and OerterGraf and others, 1991, unpublished data).

Much less is known about the accumulation history of marine ice at the bottom of the ice shelf. In accordance with field measurements presented by Reference ThyssenThyssen (1988) and numerical model simulations by Determann (1991) and Reference Hellmer and OlbersHellmer and Olbers (1991), we have assumed that accretion of marine ice takes place at a rate of 1.2 m a⁻¹ (ice) between 350 and 230 km upstream of the drilling location. For a further 180 km along the flowline, no net accumulation occurs. Melting sets in 50 km upstream of the drilling site BÍ3 with melt rates increasing linearly from 0 to 5 ma⁻¹ (Reference DetermannDetermann, 1991). Based on the results presented in the next section, particle paths in the marine-ice layer have been approximated by linear functions.

4.2 Comparison between observed grain-boundary densities and simulation results: meteoric ice layer

The textural development of the meteoric ice sampled at different depths in the core is governed by the accumulation of strain due to ice-shelf flow and the minimization of free surface energy. The macroscopically prominent effects of the former process include wavy extinction, polygonization of grains and, finally, dynamic recrystallization (for a comprehensive discussion of the effects of stress and temperature on ice texture and fabric refer to: e.g. Reference Budd and JackaBudd and Jacka, 1989; Reference AlleyAlley, 1992). Minimization of free surface energy is brought about by growth of grains associated with movement of high-angle grain boundaries (e.g. Reference GowGow, 1969; Reference PatersonPaterson, 1981; Reference AlleyAlley, 1992). For roughly isothermal firn and ice that has undergone negligible strain other than internal compaction, the resulting change in grain-size has been shown to obey an Arrhenius-type relationship (Reference GowGow, 1969). The combined effect of dynamic recrystallization and grain growth is at present not well understood. Here, we will first try to assess the potential influence of thermodynamic processes by computing grain growth for the variable temperature history of ice sampled at Β13. As a second step, we will compare simulated and observed grain-sizes with respect to the strain history.

As shown by Reference GowGow (1969) for samples of Antarctic firn and ice under low or no deviatoric stress, growth of grains of initial cross-sectional area A ₀ can be described by

with a growth rate of k (mm² a⁻¹) and a final cross-sectional area A at time t. The dependence of the growth rate k on temperature Τ is best described by

k ₀ being a constant, R the universal gas constant of 8.314 J mol⁻¹ K⁻¹, Q an activation energy and Τ the temperature in K. Thus, for a temperature history T(t) derived from the particle-path model described in the previous section, we can compute A at a time t′ with an initial grain-size A ₀ of 1 mm² at time t₀ as observed in the upper firn layers, according to

Based on the polar-firn data compiled by Reference PatersonPaterson (1981, p. 18), Q is taken as 42.3 kJ mol⁻¹ and k ₀ as 8.3 × 10⁶ mm² a⁻¹.

Figure 8 presents the result of such a computation in combination with the data on meteoric ice obtained from the core. Note that grain-boundary density Βχ has been derived from computed grain-sizes as well as those measured manually, assuming uniform grain cross-sections of hexagonal (i.e. plane-filling) shape. While the computed curve reproduces the general trend of decreasing grain-boundary density with age, a closer inspection of measured and computed data indicates that, at least for the age span 300-1300 years, a computation based on grain growth overestimates Β _A, i.e. grain-sizes are larger than expected from thermodynamic growth alone. The growth rate, however, is reproduced fairly well up to an age of 1300 years, corresponding to a cumulative vertical strain (ΔΖ/z ₀) of c. 70%. Older ice exhibits little or no systematic change in Β χ or A_mean. Sensitivity studies demonstrate that the observed age/grain-boundary density distribution is very little affected by fluctuations in ice velocities or accumulation rates, partly due to the counterbalance between the younger age of ice for higher velocities and accumulation rates, on the one hand, and enhanced grain growth due to faster burial of ice, on the other.

Comparatively little information is available on the combined effects of stress and thermodynamic processes on the grain-size of ice. Reference GowGow (1963) observed a roughly linear increase of grain cross-sectional area with depth in an ice core from the Ross Ice Shelf. In their study of a core from Byrd Station, Reference Gow and WilliamsonGow and Williamson (1976) reported increasing grain-sizes to a depth of about 600 m, near-constant or decreasing grain-sizes from 600 to 1600 m depth and a further most distinct increase in the highly strained bottom 500 m. For the Vostok core, Reference Lipenkov, Barkov, Duval and PimientaLipenkov and others (1989) observed an increase in grain-size with depth even in significantly strained ice (see also discussion by Reference AlleyAlley (1992)). From this study, it appears that, irrespective of vertical strains up to 65%, the grain-size profile is compatible with the thermal history of the ice. The observed c-axis distribution patterns (random up to a depth of roughly 40 m corresponding to 20% vertical strain and clustering into a vertical plane below) demonstrate the effects of basal glide in individual grains. Strain is accommodated locally through polygonization and sub-grain formation which are distinct below roughly 95 m depth in the core. While these processes result in a size decrease of a given grain population (and an increase in grain-boundary density), this effect is largely compensated by grain growth and dynamic rccrystallization, as indicated by the complex, bulging grain shapes dominant in the lower half of the meteoric layer ( Fig. 5a). At depths below about 120 m (corresponding to ages older than 1300 years and vertical strains > 65%) grain-boundary densities assume near-constant values around 0.7 mm⁻¹ (grain-sizes of approximately 30 mm²). Such attainment of stationary grain-sizes has been described by Reference JackaJacka (1984) from laboratory experiments. He showed that, in the tertiary-creep regime at temperatures between −7.1° and −10.6°C, grain-sizes generally decrease (an increase was noted only for one set of very fine-grained samples) to an equilibrium size of roughly 2.2.5 mm, i.e. far below the sizes encountered in the BÍ3 core. As temperatures are lower by 10° to 18°C in the Ronne Ice Shelf, it appears that low stresses are responsible for attainment of such large values of A_8tat in this case. Thus, for conditions representative of the Ronne Ice Shelf (−20°C, octahedral shear stress of 0.05 MPa and strain rate 10⁻³ a⁻¹), the compilation of data by Reference Budd and JackaBudd and Jacka (1989, Fig. 10) indicates a stationary grain-size of 10 mm linear dimensions, i.e. the same magnitude as observed in the core ( Fig. 3).

4.3 Comparison between observed grain-boundary densities and simulation results: marine-ice layer

The grain-boundary densities ( Fig. 11) that have been computed for the marine-ice layer as outlined in section 4.1 demonstrate that the profiles change drastically during the no-accretion and ablation regimes. The simulation shows that grain-boundary densities increase with depth as long as ice is accumulated from below (i.e. grain-size proportional to age as generally observed in ice sheets). During the no-accretion and ablation stages, however, grain growth is favoured in the lower ice layers where temperatures are elevated. As a consequence, at the drilling location, the simulation shows Β _A is constant with depth. Thus, longer residence times at higher temperatures are at least part of the explanation for the paradoxical observation of grain-sizes decreasing with age. However, the increasing values of Β _A towards the top of the marine layer cannot be adequately explained by the simulation. Possibly, though unlikely as shown below, this increase towards the top could reflect differences in the initial size of the crystals accreting at the ice-shelf bottom.

Fig. 11. Grain-boundary density profiles of the marine-ice layer (y axis shows depth below meteoric—marine-ice transition). Dots show automatically determined thin-section data, crosses are converted manual measurements of grain area. Dashed and solid lines demonstrate temporal development of profiles progressing through the zones of accumulation (0–120 km away from the onset of accumulation; see also Fig. 1), zero accretion (120–300km) and ablation (300–350km).

Much more important with regard to grain growth are the insoluble, particulate inclusions ubiquitous in the upper layers. Several studies have dealt with the inhibition of grain growth owing to microparticle inclusions. Amongst others, Reference Gow and WilliamsonGow and Williamson (1976) found layers of volcanic ash coinciding with a drastic decrease in crystal size, attributed partly to the inhibitive effect of high microparticle concentrations. According to measurements made by Reference Kyle, Palais and DelmasKyle and others (1982) on the Byrd Station core, particle concentrations in these dust layers are generally lower than those in the Ronne Ice Shelf (volume fractions in the range of 2 × 10⁻⁷ with maxima near 5 × 10⁻⁵ as compared to 10⁻³ to 5 × 10⁻² gl⁻¹; personal communication from R. Petschick). Reference Alley, Perepezko and BentleyAlley and others (1986) developed a theory of grain growth in polar ice under low stress in the presence of microparticles. They derived an equation relating the ratio of the particle-drag force to the intrinsic (i.e. in the absence of solid impurities) driving force P _p/P _i to volume V _p and radius r _p of particles

for ice of average grain radius R. With mean particle sizes between 0.5 and 50μm and volume fractions between 10⁻⁵ and 10⁻⁴, and ice-grain radii around 5 mm, Ρ _p/Ρ _i takes on values between roughly 2 × 10⁻³ and 2 (P_P/Pi describes the reduction in grain-growth rate as shown by Reference Alley, Perepezko and BentleyAlley and others (1986)), indicating potentially mild to drastic retardation of grain growth for smaller particle sizes. Interpretation of computed ratios P _p/P _i is complicated by the effects of (1) strain, which is not accounted for in theory; (2) coagulation of clay minerals during ageing resulting in particle-radius increase; (3) retainment of particles at triple-grain junctions, where they are of less influence on grain growth; and (4) enhanced concentrations of microparticles in grain-boundary zones. These limitations notwithstanding, the upper marine-ice layers should in theory experience restriction of grain growth. In practice, additional evidence is provided by the arrangement of elongated crystals into horizontal rows bounded by strings and layers of sediment, a feature which is not observed in the meteoric ice just above the discontinuity. Also, the predominance of the 0-2 mm size fraction in the marine ice with high solid impurity content ( Fig. 6c) indicates that, even for small crystals with highly curved boundaries, the force driving grain growth is compensated by impurity drag. More important still, ice at roughly 70 m depth, within the meteoric layer, exhibits significantly lower grain-boundary densities than at the top of the marine-ice layer (see circled data points in Figure 3), even though the marine ice has experienced much higher temperatures favouring grain growth and dynamic recrystallization. Since the deformational history of these layers is comparable (meteoric ice at 70 m depth has been deposited near the point along the flowline where bottom accumulation sets in), we have to conclude that it is the solid impurity content that prevents more vigorous grain growth in the marine as compared to the meteoric ice. The concurrent increase in grain-boundary density and salinity towards the top of the marine ice might suggest a potential influence of salinity; yet, results from a second core taken in the Ronne Ice Shelf that is currently being processed, demonstrate that the sediment and not the salt is crucial in determining grain-size. In the second core, grain-sizes are observed to increase sharply (factor > 3) as one passes from a zone of high silt content at 158.5 m depth to a layer that contains little or no sediment at 153.5 m at the very top of the marine-ice layer, while salinity does not vary significantly between the two. Similar observations have been made on the series of eight closely spaced thin sections from Β13, where electrolytical conductivity measured on melted thin-section segments was not observed to correlate with grain-size. These findings are supported by laboratory experiments conducted by Reference Achaval, Nasello and CeppiAchaval and others (1987) at temperatures between −16° and −2°C, who demonstrated that NaCl concentrations between 10⁻⁴ and 10⁻² M (0.006–0.6%) enhance grain-growth rates. As will become clearer below, the explanation for a parallel trend in salinity and grain-boundary density may therefore lie in the early history of initial ice accretion underneath the ice shelf. Liquid impurities are also important in softening the basal ice layer, based on the observations made by Reference DuvalDuval (1977), who measured an increase in shear rates of temperate ice by a factor of approximately 1.4 as the water content rose from nil to 0.05%.

4.4 Evolution of the salinity distribution and mechanisms of basal accretion

One of the most telling pieces of evidence for the marine origin of the basal ice is the δ ¹⁸O values, which increase from −40 to +2% at the transition from meteoric to marine ice (Reference OerterOerter and others, 1992). The latter value corresponds to that expected for equilibrium fractionation upon freezing of sea water circulating under the ice shelf. This does not explain the extraordinarily low salinity of the marine-ice layer which ranges roughly two orders of magnitude below values from sea ice or from basal ice underneath the Ross and Ward Hunt Ice Shelves. Anomalously low ice salinities may, in principle, be traced back to two potential causes: highly reduced incorporation of salt upon ice formation or vigorous loss of salt during later desalination. The wealth of research conducted within the sea-ice community allows us to assess the magnitude of either one of them (see Reference Weeks, Ackley and UntersteinerWeeks and Ackley (1986) for a thorough review of this work).

The initial salinity S _i of an ice layer grown from sea water of salinity S _W is determined by an effective distribution coefficient k _eff such that

From the experimental work of Reference Lofgren and WeeksLofgren and Weeks (1969), we obtain an estimate of k _eff = 0.15 for growth velocities of approximately 3 m a⁻¹ for columnar sea ice (i.e. congelation of sea water at the ice—water interface). For slower growth rates, k _eff approaches a minimum near 0.12 for sea ice (Reference Weeks, Ackley and UntersteinerWeeks and Ackley, 1986). While ice grown from dilute salt solutions at very slow rates may incorporate much less salt during growth, this does not apply for the salinity and growth-rate regime encountered beneath the ice shelf where marine ice accretes with rates of decimetres to more than 1 ma⁻¹ (for constraints on accretion rates see section 4.1; Reference DetermannDetermann, 1991; Reference Hellmer and OlbersHellmer and Olbers, 1991). Other growth mechanisms, such as consolidation of frazil crystals, correspond to distribution coefficients larger or at best equal to those shown above because of similar or higher porosities of frazil as compared to ordinary congelation ice (see also Reference Weeks, Ackley and UntersteinerWeeks and Ackley, 1986). Hence, the most conservative estimate of k _eff = 0.10 yields an initial salinity of roughly 3.4% for the marine ice, i.e. more than two orders of magnitude above the actual values.

As a newly accreted layer of sea ice ages and cools due to additional growth below, a net export of salt occurs through a combination of three different brine-drainage mechanisms (Reference Weeks, Ackley and UntersteinerWeeks and Ackley, 1986). One is the expulsion of brine upon cooling due to the differential decrease in porosity. Based on the equations of Reference Cox and WeeksCox and Weeks (1986), it can be shown that for the temperature gradients encountered in the marine-ice layer, brine explusion would lower the initial layer salinity by a factor of 0.85 at maximum (cooling from −2° to −14°C, as measured at the bottom of the B13 hole). This is still more than one order of magnitude higher than values found in the lower part of the core. Furthermore, whereas brine is easily expelled from sea ice through brine channels or cracks, it is not clear how brine could be expelled over vertical distances of several tens of metres through the marine ice column without any traces discernible in the core (neither in the two cores drilled in the Ronne Ice Shelf nor the one taken from the Amery Ice Shelf). As sea ice is cooled from the top, the density of brine increases upwards within an ice layer. In a process referred to as gravity drainage, the brine may be replaced by less-dense sea water, inducing a bulk-salinity decrease that is controlled by the local temperature gradient. The latter amounts to roughly 0.06°C m¹, inducing a desalination rate of 0.3%a⁻¹ (Reference Cox and WeeksCox and Weeks, 1988). However, gravity drainage ceases once pores are not in hydraulic connection with the water column. For ordinary sea ice, this connection appears to be terminated at brine-volume fractions below 50% (Reference Cox and WeeksCox and Weeks, 1988), implying that gravity drainage could only explain a decrease of marine-ice salinities to not less than 1.5%. Finally, brine-filled pores migrate in a temperature gradient due to freezing at the cold and melting at the warm wall of the cavity. Based on the work by Reference Hoekstra, Osterkamp and WeeksHoekstra and others (1965) and Reference SeidenstickerSeidensticker (1966), maximum migration velocities should at maximum amount to roughly 2 mm a⁻¹ (at the bottom of the marine-ice layer).

Since the desalination rates resulting from any combination of these known desalination mechanisms are too low by at least two orders of magnitude, we are led to believe that the anomalously low salinities in the marine ice can only be explained by low initial salinities S _i of newly accreted ice layers. Based on the isotopic composition of the marine ice (indicating no incorporation of low-salinity glacial meltwater) and thermodynamic constraints (conductive heat flux in the central Ronne Ice Shelf on the order of 0.1 W m⁻²), we conclude that accretion of ice at the base takes place without significant in-situ ice growth. In addition, the accretion mechanism has to be associated with anomalously low salt-distribution coefficients (k _eff mostly <0.001), fundamentally different from those observed in ordinary sea ice. In view of the work of Kipfstuhl and others (1992), the mechanism in question is most likely associated with the accumulation of ice crystals beneath the ice shelf. Kipfstuhl and others have shown that ice crystals formed under water may constitute the marine-ice layers of Antarctic ice shelves. Such centimetre-sized ice platelets have been encountered at greater depths in front of the ice shelf by Reference Alley and BentleyDieckmann and others (1986) and are thought to accumulate in thick layers at the ice-shelf bottom. Indirect field evidence suggests an ice—water mixture is present at the base of the ice shelf, even though direct observations of this ice are still lacking to date (Reference Engelhardt and DetermannEngelhardt and Determann, 1987; Reference Nicholls, Makinson and RobinsonNicholls and others, 1991). In the absence of significant in-situ ice growth, these layers have to consolidate under the deviatoric buoyancy stress (c. 0.02 MPa at the top of a 25 m crystal layer with an assumed 75% packing density) exerted by the tens of metres of crystals accumulating below. Densification and expulsion of brine would then take place through fragmentation and settling of platelets analogous to firn densification. Since ice platelets are essentially free of salt inclusions, brine only has to drain from intergranular boundaries. In addition, local uniaxial stress may cause impinging crystals to melt and recongeal within voids, with a corresponding decrease in brine-volume fractions (see Reference LaChapelleLaChapclle (1968) for a discussion of the phenomenon).