Using a composite flow law to model deformation in the NEEM deep ice core, Greenland: Part 2 the role of grain size and premelting on ice deformation at high homologous temperature

The ice microstructure in the lower part of the North Greenland Eemian Ice Drilling (NEEM) ice core consists of 10 relatively fine grained ice with a single maximum crystallographic preferred orientation (CPO) alternated by much coarser grained ice with a partial (great circle) girdle or multi-maxima CPO. In this study, the grain size sensitive (GSS) composite flow law of Goldsby and Kohlstedt (2001) was used to study the effects of grain size and premelting (water-like layer along the grain boundaries) on strain rate in the lower part of the NEEM ice core. The results show that the strain rates predicted in the fine grained layers are about an order of magnitude higher than in the much coarser grained layers. The dominant 15 deformation mechanisms, based on the flow relation of Goldsby and Kohlstedt (2001), between the layers is also different with basal slip rate limited by grain boundary sliding (GBS-limited creep) being the dominant deformation mechanism in the finer grained layers, while GBS-limited creep and dislocation creep (basal slip rate limited by non-basal slip) contribute both roughly equally to bulk strain in the coarse grained layers. Due to the large difference in microstructure between finer grained ice and the coase grained ice at premelting temperatures (T>262K), it is expected that the fine grained layers deform 20 at high strain rates, while the coarse grained layers are relatively stagnant. The difference in microstructure, and consequently in viscosity, between impurity-rich and low impurity ice can have important consequences for ice dynamics close to the bedrock.

finer grains. In case of the NEEM ice core, the alternated layers of fine and coarse grained ice are the results of stratigraphic disruptions and overturned folds, which consist of low impurity Eemian interglacial ice and impurity-rich ice from the late Eemain and from the penultimate glacial period (Figure 1) (NEEM community members, 2013).
These coarse grained layers at the bottom of some polar ice cores typically possess crystallographic preferred orientations (CPOs) that could be described as a multi maxima, although the exact type of CPO is often unclear due to the low 5 number of grains measured in individual thin sections. The coarse grains and multi maxima CPO are thought to be the result of rapid strain induced boundary migration (SIBM) in combination with the nucleation of new grains (SIBM-N) (e.g. Alley, 1992;Duval and Castelnau, 1995;Durand et al., 2009;Faria et al., 2014a), where based on the coarse grain size SIBM is likely more important than nucleation of new grains. SIBM is the migration of grain boundaries driven by the difference in stored strain energy between neighbouring grains that result from lattice distortions such as dislocations (Humphreys and Hatherly, 10 2004). SIBM starts in firn (Kipfstuhl et al., 2006(Kipfstuhl et al., , 2009 and is assumed to increase grain size (e.g. Duval and Castelnau, 1995), although under certain conditions SIBM can also be a grain size reducing mechanism by grain dissection (Steinbach et al., 2017). The layers of alternating grain size in deeper NEEM samples allows for the study of the effect of grain size on strain rate and CPO development, in the high temperature regime where enhanced creep and recrystallization can be explained by the occurrence of premelting along grain boundaries . 15 In this study, the composite flow law of Goldsby and Kohlstedt (2001) was used to explore the effect of grain size on strain rate in the lower part of the NEEM ice core. The composite flow law describes the deformation of polycrystalline ice as a combination of grain size sensitive (GSS) and grain size insensitive (GSI) deformation mechanisms, where the dominant deformation mechanism depends on the temperature, stress and grain size. Compared to our companion paper (part 1), which describes ice deformation at relatively low temperatures in the upper 2207 m of the NEEM ice core, the emphasis in this paper 20 is on possible differences in the controlling deformation mechanism close to the melting point. The results from flow law calculations were combined with CPO data to study deformation mechanisms in the lower part of the NEEM ice core. The NEEM ice core was chosen because of the high density of reflective light microscopy (LM) images (Kipfstuhl, 2010;Binder et al., 2013) and the alternation of fine and coarse grained layers in the lower part of the ice core. These reflective LM images were used to determine the change in grain size with depth (Binder, 2014). Furthermore, the CPO data of the NEEM ice core 25 (Eichler et al., 2013) were available. A critical assessment of the temperature threshold for the onset of enhanced recrystallization and creep, caused by premelting, in polar ice sheets led to a modification of the composite flow law of Goldsby and Kohlstedt (2001). The NEEM ice core data were used to calculate the strain rate predicted by Glen's flow law (Glen, 1952, ice to be alternated with the finer grained late Eemian ice. Below 2432.2 m of depth, in the lowest 330 m of the NEEM ice core there is undated finer grained, impurity rich ice that is thought to be from the penultimate glacial. In the remainder of this study, the ice from 2207 m of depth to the ice-bedrock interface at 2540 m of depth will be referred to as the 'Eemian-glacial facies'.
The lower part of the glacial ice of the NEEM ice core, from 2000 to 2207 m of depth was included in this study to 5 show the contrast in grain size, CPO and calculated strain rate between the glacial ice and the deeper Eemian-glacial facies. Therefore, the available LM images, orientation images and CPO data below 2000 m of depth were included in this study.
Calculations using the GSS composite flow law of Goldsby and Kohlstedt require grain size as an input variable. The grain size data in the lowest 540 m of the NEEM ice core were obtained using 224 large area scanning macroscope (LASM) images (Kipfstuhl, 2010) taken using reflective light macroscopy (Krischke et al., 2015). This method uses thermal etching by 10 sublimation to reveal (sub)grain boundaries as grooves on the surface of the ice core sample (e.g. Saylor and Rohrer, 1999) and has a resolution of 5 µm per pixel edge. Each LASM image is about 90 mm long by about 55 mm wide (Kipfstuhl et al., 2006) and was digitally analyzed using the Ice-image software (www.ice-image.org) (Binder et al., 2013;Binder, 2014). The software automatically detects the grain area of each grain by counting the pixels enclosed by grain boundaries. The total area classified as 'grain' by the Ice-image software was divided by the number of grains to give a mean area. The equivalent grain 15 diameter was calculated from the mean area; this is always larger than the mean diameter calculated from the population of diameter measurements. Deriving a full grain size distribution, as was done in the companion paper (part 1), was not possible in the Eemian-glacial facies because the number of grains in the LASM images (90 x 55 mm) of the coarse grained layers was too low. Grains with a diameter <0.3 mm were excluded from the data set as these grains are often artefacts caused by relaxation (Binder, 2014). In some parts of the Eemian-glacial facies, the grains are up to several centimetres and the grain boundaries 20 are irregular with many grain boundary bulges. It is not possible to determine a mean grain size for these ice core sections by the Ice-image software as these grains often cross the edge of the LM images and are therefore not included in the grain size data (Binder, 2014). After visual inspection of the LASM images to check the grain size, the ice core sections containing very large grains were assigned a mean grain diameter of 30 mm, which was the estimated grain diameter based on the LASM images. 25 An automatic Fabric Analyzer (FA) was used to create high-resolution maps of the c-axes orientations. The method is based on the double-refracting properties of the hexagonal ice crystal. It offers a fast alternative for the measurement of crystal orientations, which are, however, limited only to the c-axes. The grains in each orientation image were plotted in a pole figure. For each orientation images the Woodcock parameter, k, was calculated according to (Woodcock, 1977): where λ 1 , λ 2 and λ 3 are the normalized eigenvalues of the second order orientation tensor with λ 1 < λ 2 < λ 3 . The Woodcock parameter is often used in order to distinguish between cluster and girdle type of CPOs. A distribution with a Woodcock parameter >1 indicates a cluster, while a Woodcock parameter <1 indicates a girdle. Further computer-based analysis (Eichler et al., 2013) of the FA-CPO-maps enables the derivation of a variety of microstructural parameters, such as mean grain shape or size. These can be used as complementary values to the LASM analysis data. However, these microstructural parameters 35 can differ significantly from the microstructural parameters obtained by the Ice-image software (www.ice-image.org) (Binder et al., 2013;Binder, 2014). For instance, the effective diameter derived from the orientation images in this study is systematically shifted towards lower values, which is mainly caused by the exclusion of grains with a grain diameter <0.3 mm in the LASM method as was described above. In the remainder of this paper, the grain size (effective diameter) determined using the Ice-image software (Binder et al., 2013;Binder, 2014) will be used unless stated otherwise. 40

Flow laws and flow law parameters
One of the two flow laws that was used during this study is the composite flow law of Goldsby and Kohlstedt (2001). The composite flow law was derived during uniaxial deformation tests in secondary creep with very fine grained ice Kohlstedt, 1997, 2001). The composite flow law combines different deformation mechanisms of ice explicitly, instead of presenting a series of individual flow laws. During their uniaxial deformation experiments on artificial fine grained ice in 5 secondary creep, Kohlstedt (1997, 2001) defined a composite flow law with rate contributions from four mechanisms: where ε̇ is the strain rate. ε̇d isl refers to dislocation creep where basal slip is the main strain producing mechanism which is rate limited by non-basal slip andε̇d iff refers to diffusion creep. Basal slip and grain boundary sliding are sequential processes 10 acting together, where the slower mechanism determines the overall strain rate by rate limiting the faster mechanism (Durham and Stern, 2001). In the part in between brackets in equation (2), ε̇ refers to basal slip, while ε̇G BS refers to GBS. Under stress, grain size and temperature conditions appropriate for terrestrial ice, diffusion creep and grain boundary sliding rate limited by basal slip are not relevant for ice deformation (Goldsby and Kohlstedt, 2001;Goldsby, 2006). Therefore, the composite flow law simplifies to: 15 The strain rate produced by creep can be described by the following general flow law: where ε̇ is the strain rate (s -1 ), A is a material parameter, σ is the stress (MPa), n is the stress exponent (dimensionless), is the grain size (m), is the grain size exponent (dimensionless), Q is the activation energy (kJ mol -1 ), R the gas constant (J K -1 20 mol -1 ) and T the absolute temperature (K) corrected for the change in pressure-melting point due to the cryostatic pressure.
The value for p determines whether the creep is grain size insensitive (p=0) or grain size sensitive (p≠0). The mean grain diameter, as determined from LASM images with the Ice-image software, was used for the calculation of the strain rate produced by GBS-limited creep.
If the temperature is expressed in terms of the difference with the pressure-melting point, ice can, as a first order 25 approximation, be considered incompressible (Rigsby, 1958;Doake andWolff, 1985, Greve et al., 2014). The pressure-melting temperature was calculated according to: where is the pressure-melting temperature (°C), is the pressure-melting constant for glacier ice (9.810 −8 °C −1 ; Lliboutry, 1976) and ∆ is the overburden pressure (Pa) which was calculated according to: 30 where is the density of ice (910 kg m -3 ), ℎ is the ice thickness (m) and is the gravitational constant (9.81 m s -2 ). The in-situ temperature ( ) profile of the NEEM ice core was taken from Sheldon et al. (2014). In the remainder of this paper, * is used for the difference in temperature of the ice at a certain depth with respect to the pressure-melting point at that depth, which can be calculated according to 35 compression experiments on artificial, (initially) isotropic polycrystalline ice. Glen's flow law has the same form as Equation (4), but is independent of grain size (i.e., p=0) and the form of Glen's flow law that is most often used has a stress exponent of n=3 (Paterson, 1994). However, at the low stress conditions with strong CPO development, a higher value of n of 3,5-4 might be a better approximation of ice dynamics in polar ice sheets as was shown by Treverrow et al. (2012), Bons et al. (2018 and others. 5 Following the analysis presented in our companion paper (part 1), a constant equivalent stress of 0.07 MPa was taken as input for Glen's flow law and the composite flow law. This assumption is a useful first approximation for the NEEM ice core where the equivalent stress, related to the shear stress in the lower part of the ice core, is by coincidence similar to the magnitude of equivalent stress related to the vertical stress in the upper part of the ice core. We explore the effect of grain size on the 10 dominant deformation mechanism and the total strain rate, it is beyond the scope of this study to derive a stress-depth model for NEEM because this requires knowledge on the rheology, which is the property that is investigated here. When calculating strain rates, no distinction is made between simple shear and pure shear deformation.  Montagnat et al., 2014), almost all c-axes are strongly aligned parallel to the vertical ice core axis. However, compared to the glacial ice, the grain size of the ice core section in Figure 2a is slightly larger 25 and the grain shape is more irregular. The ice core section in Figure 2b is one of the ice core sections that was given a mean grain size of 30 mm, typical of the Eemian ice with high δ 18 Oice and low impurity content deposited unders warm interglcial conditions (NEEM community members, 2013). The grains have an irregular shape with many millimetre sized bulges along the grain boundaries. The orientation image and pole figure show that the c-axes are distributed in a partial (great circle) girdle spanning about 40° from the vertical axis. Although in some cases the c-axes distribution can also be classified as a multi 30 maxima CPO. The ice core section in Figure 2c has a mean grain size of about 7 mm and originates from the end of the Eemian period (NEEM community members, 2013). The grain boundaries are bulging and have an irregular shape. The orientation image and pole figure show that the c-axes are distributed in a partial (great circle) girdle spanning about 30° to 40° from the vertical axis.

Correlation mean grain diameter with type and strength of CPO 35
The correlation between the mean grain diameter and the type and strength of CPO in the lowest 540 m of the NEEM ice core is shown in Figure 3a and 3b. This figure shows the first c-axes eigenvalue, λ 3 in equation (1) (Eichler et al., 2013) and the Woodcock parameter (Woodcock, 1977) versus the mean grain diameter for each orientation image in the lower part of the glacial ice (2000-2207 m of depth) and the ice in the Eemian-glacial facies (2207-2540 m of depth). The ice from the lower part of the glacial period (2000-2207 m of depth), which has a finer mean grain diameter (about 2 mm) than the ice in the 7 Eemian-glacial facies, has a c-axes eigenvalue of λ 3 >0.9 and the Woodcock parameter typically varies from 4-10. Some of the finest grained regions in the Eemian-glacial facies have a slightly larger mean grain diameter (3-5 mm) with a similar c-axes eigenvalue of λ 3 >0.9 and a rather similar Woodcock parameter of about 2-10. For ice core sections with a mean grain diameter larger than about 5 mm, the eigenvalue is λ 3 <0.9 with a Woodcock parameter varying from 0.3-10. However, the number of grains per orientation image decreases with increasing grain size and therefore the statistical significance of the first eigenvalue 5 and Woodcock parameter decreases with increasing mean grain diameter. Based on Figure 3, two classes of microstructure can be distinguished based on mean grain diameter and type and strength of CPO. The first class has a relatively fine mean grain diameter of <5 mm that is comparable in eigenvalue and Woodcock parameter to the glacial ice (green rectangle). The other class has a mean grain diameter of >5 mm with a relatively low first eigenvalue and Woodcock parameter (yellow rectangle). The mean grain diameter in Figure 3 was derived from orientation images, which gives a slightly lower mean grain 10 diameter than the mean grain diameter derived using the Ice-image software, like Figure 2. Table 1 shows data from eight polar ice cores drilled at the Greenland and Antarctic ice sheets that contain a sudden increase in grain size and change in CPO in the lower part of the ice core. The in-situ temperature at the bottom of the boreholes varies significantly between the ice cores. The ice near the bedrock at GISP2 and GRIP was frozen to the bed, while for Byrd, EDC, 15 EDML, NEEM and Siple dome the ice was at, or very close to, pressure-melting point. In all eight ice cores, the CPO and grain size start to change at an in-situ temperature of about -13°C (260K). For the NEEM ice core, this transition coincides with the climatic transition of the end of the Eemian period, also known as marine isotope stage (MIS) 5e, to the beginning of last glacial period (MIS 5d). The transitions to coarse grains with a multi maxima CPO in the EDML, GISP2 and GRIP ice core also coincides with a climatic transition. For the other four ice cores, the transition to a different microstructure does not 20 coincide with a major climatic transition. The pressure corrected temperature threshold (T*, Equation 5-7) at which this transition occurs in these polar ice cores is remarkably constant at T* of -11°C (262K). The depth in the ice cores at which the microstructure changes to large grains and a multi maxima CPO is different for each ice core, which leads to a slightly different T* when correcting for the change in pressure-melting point with depth (Equation 5-7). However, when taking into account the uncertainty in determining the in-situ temperature at a certain depth and the possible influence of the different impurity 25 content between the ice cores and individual layers in the same ice core that affect the pressure-melting point, the effect of correcting the temperature at which the microstructure changes due to changes in overburden pressure is small. A different cause for the sudden change in ice microstructure is stress relaxation due to the disruption of simple shear flow by the bedrock topography. This leads to more stagnant ice which, at the elevated temperatures close to the bedrock, can start to recover and recrystallize. However, the alternation of different microstructures with finer and coarser grained as found at NEEM cannot 30 be explained in this way.

Transition temperature: NEEM results compared to other polar ice cores
The flow law parameters of the original composite flow law (Goldsby and Kohlstedt, 2001) shown in Table 2 were modified to fit the temperature (T*) threshold of -11°C (262K) for premelting as derived from Table 1 and the experimental data points from Goldsby and Kohlstedt (2001). Another reason for modifying the dislocation creep parameters is improve the fit of the dislocation creep flow law and the experimental data of Goldsby and Kohlstedt (2001) as explained in the companion 35 paper (part 1). Both the flow law parameters for dislocation creep and GBS-limited creep were modified and are given in Table   3. Since the flow law parameters for GBS-limited creep were adjusted to be consistent with a temperature (T*) threshold of 262K, they are different from the flow law parameters used in our companion paper. Figure 4 shows the temperature versus the calculated strain rate using the original flow law parameters of Glen's flow law (Paterson, 1994) and the members of the modified flow law parameters of the composite flow law (Table 3). The calculated 40 strain rates for Glen's flow law, dislocation creep and GBS-limited creep increase with increasing temperature and show a kink at their temperature threshold of 263K (Glen's flow law) or 262K (modified composite flow law). The strain rate increase with temperature of the GBS-limited creep mechanism above the temperature threshold of 262K is considerably higher than for the dislocation creep mechanism or Glen's flow law, although this difference is largely related to our choice of Paterson's (1994) version of Glen's flow law. Using the Budd and Jacka (1989) description for the temperature sensitivity of Glen's law, would produce different results. Figure 5 shows the calculated strain rates, along with the relevant microstructural data (Binder et al., 2013;Eichler et al., 2013;NEEM community members, 2013;Binder, 2014). The modified composite flow law shows that the calculated strain rate in the lower part of the glacial ice, which reaches to a depth of 2207 m (NEEM community members, 2013), is about 2.510 −11 s −1 and the CPO has a strong single maximum. The dominant deformation mechanism of the modified composite flow law in the lower part of the glacial ice is GBS-limited creep, with only a very small contribution of dislocation creep to 10 bulk strain rate. Glen's flow law predicts a higher strain rate (about 10 −10 s −1 ) than the modified composite flow law in the lower part of the glacial ice. At the interface between the glacial ice and Eemian-glacial facies, the calculated strain rate for the composite flow law drops by about an order of magnitude. The relative contribution of the two members of the composite flow law changes as well with GBS-limited creep and dislocation creep contributing roughly equally to bulk strain rate. At the same depth, the CPO changes from a strong single maximum in the glacial ice to a partial girdle in the upper part of the 15

Calculated strain rates and deformation mechanisms 5
Eemian-glacial facies. The calculated strain rate of the modified composite flow law varies by about an order of magnitude between the finer and coarser grained regions close to the stratigraphic disruptions. This variation in calculated strain rate close to the stratigraphic disruptions is produced by GBS-limited creep, which is affected by the change in grain size. The strain rate produced by dislocation creep, which is not affected by the variation in grain size, steadily increases with depth throughout the Eemian-glacial facies. Glen's flow law, which is not affected by grain size variation either, predicts an increasing strain 20 rate with depth and a higher strain rate than the modified composite flow law in the entire Eemian-glacial facies. The increase in strain rate coincides with the increase in temperature along the NEEM ice core (Figure 1 companion paper).
The relative contribution of GBS-limited creep and dislocation creep to the bulk strain rate of the modified composite flow law is roughly equal for the ice core sections that were assigned a mean grain diameter of 30 mm just below the stratigraphic disruptions at 2209.6 m and 2262.2 m of depth. At deeper levels, the contribution of GBS-limited creep to bulk 25 strain rate for these coarse grained ice core sections increases. The increase in relative contribution of GBS-limited creep to bulk strain rate, at the assigned constant grain size of 30 mm, results from the lower activation energy at T>262K for dislocation creep compared to GBS-limited creep (Table 3, Figure 4). The difference in activation energy for Glen's flow law and the dislocation creep mechanism above their temperature thresholds is rather small (Table 3), which results in an almost similar order of magnitude strain rate increase with depth. The relative changes in strainrate between the different flow laws are very 30 sensitive to activation energies used (Table 3). In the case of Glen's law and possibily for the dislocation creep mechanism, a higher activation energy could apply close to the melting temperature (e.g. Budd and Jacka 1989).

Discussion
The results show that the Eemian-glacial facies consists of layers with relatively fine grains that are alternated by layers of very coarse grains. The coarse grained layers have a strongly interlocking grain boundary structure with a partial girdle or 35 multi maxima type of CPO, while the fine grained layers have a more regular grain shape and have a single maximum type of CPO (Figure 2 and 3). A comparison with other polar ice cores showed that layers with very coarse and interlocking grains with a multi maxima or partial girdle type of CPO start to appear at a T* value of about 262K ( Table 1). The modified composite flow law of Goldsby and Kohlstedt (2001) predicts that the strain rate in the fine grained layers, which is almost entirely produced by GBS-limited creep, is about an order of magnitude higher than the strain rate in the coarse grained layers, where GBS-limited creep and dislocation creep contribute roughly equally to bulk strain rate ( Figure 5).

The role of impurities in premelted ice
It is well known that changes in impurity content correlate well with changes in mean grain size in polar ice cores (e.g. Fisher and Koerner, 1986;Paterson, 1991;Thorsteinsson et al., 1995;Cuffey et al., 2000); finer grains occur in ice with a higher 5 impurity content. It is often assumed that impurities control grain size by pinning of grain boundaries (e.g. Fisher and Koerner, 1986;Gow et al., 1997;Durand et al., 2006), although the exact mechanism by which impurities control the mean grain size is still not understood in detail (Eichler et al., 2017). Similar to the Eemian-glacial facies in the NEEM ice core, the lower part of the GRIP ice core (Thorsteinsson et al., 1995) is likely affected by premelting (Table 1). In both the GRIP and NEEM ice core, the effect of impurities on grain size and shape is very large in the premelting regime (Thorsteinsson et al., 1995;NEEM 10 community members, 2013). Due to the high impurity content in the glacial ice and late Eemian ice of the Eemian-glacial facies, the mean grain size in these layers remains relatively small. On the other hand, the low impurity Eemian ice has much larger grains. The second effect of the high impurity content in the finer grained layers in the Eemian-glacial facies is the melt content along grain boundaries and triple junctions is probably enhanced due to the lowering of the pressure-melting point by salts and/or impurities (e.g. Duval, 1977;Wettlaufer, 1999a, b;Döppenschmidt and Budd, 2000). 15 Impurities also provide additional interfaces, in addition to grain boundaries, where premelting can take place. These premelting films could act as dislocation sinks that may enhance dislocation motion in ice, preventing hardening by dislocation entanglement and thus enhance the strain rate. The type of impurity can change the effectivity of premelting, but as only few studies on particle species in solid polar ice are available so far (Ohno et al., 2005(Ohno et al., , 2006Sakurai et al., 2009;2011;Oyabu et al., 2015), this argument can only be made via the total surface of impurities per volume of ice. 20

The effect of premelting on ice microstructure
Premelting is expected to initiate at grain boundaries at temperatures below, but close to, the melting point (e.g. Orem and Adamson, 1969;Döppenschmidt et al., 1998). Since premelting itself, as well as the collection of water in veins (Nye and Mae, 1972), takes place at grain boundaries and triple junctions, grain boundaries are the major 'suspect' that enables weakening in polycrystalline ice. As temperature increases, a liquid-like amorphous layer gathers in layers along grain 25 boundaries and veins along triple junctions, the presence of a liquid-like amorphous layer correlates with strain rates that are faster than predicted by extrapolation of low temperature results using the Arrhenius relation with a fixed activation energy (e.g. Mellor and Testa, 1969;Nye and Mae, 1972;Duval et al., 1977;Dash et al., 1995;De la Chapelle et al., 1999). Therefore, a flow law that is calibrated at lower temperature cannot simply be applied under premelting conditions, since the mechanical properties of the material at premelting temperature, apparently, are different. Due to the higher grain boundary surface area 30 per unit of volume in a fine grained sample, the influence of premelting on a fine grained sample is expected to be stronger than for a coarser grained sample.
A small liquid-like amorphous layer at the grain boundaries may account for the increase of grain boundary mobility by about two to four orders of magnitude (De la Chapelle et al., 1998). Since grain boundary velocity is a function of grain boundary mobility and the driving force for grain boundary migration (e.g. Higgins, 1974;Alley et al., 1986), it is expected 35 that a strong increase in grain boundary mobility leads to an increase in grain boundary velocity, provided that the stored strain energy for SIBM in the ice polycrystal is high enough. Ice deformation tests have indeed shown that grain boundary migration rates are high close to the melting point (e.g. Wilson and Zhang, 1996;Breton et al., 2016). Microstructural changes ocurring in ice close to the melting point that creates very coarse and interlocking grains, and a change in deformation behaviour, could both well be explained by the presence of a liquid-like amorphous layer that increases grain boundary mobility and 40 consequently enhances SIBM. This enhanced SIBM would result in very coarse grains with an interlocking grain boundary structure (e.g. Duval and Castelnau, 1995;Schulson and Duval, 2009;Breton et al., 2016), as observed in the layers with low impurity content of the Eemian-glacial facies (Figure 2b).
In addition to the effect of high temperature on grain boundary mobility, the cryostatic pressure in the lower part of polar ice cores (20-23 MPa for NEEM, Equation 6) will further enhance grain boundary mobility (Breton et al., 2016). Directed growth of migrating grain boundaries along subgrain boundaries in specimens deformed at a cryostatic pressure of 20 MPa 5 can lead to a smaller median grain size and a more interlocking microstructure. The smaller grain size of samples deformed at a high cryostatic pressure of 20 MPa compared to samples deformed at atmospheric pressure could be caused by grain dissection (Breton et al., 2016;Steinbach et al., 2017), since this process also depends on SIBM.
The similarity between microstructures with coarse interlocking grains in the lower part of polar ice cores (Table 1, Figure 2b) and the ice microstructure developing during deformation tests close to the melting point suggests that these 10 microstructures are governed by the same processes. It is therefore proposed that the sudden appearance of the coarse grains with an interlocking grain boundary structure in the lower part of polar ice cores is the result of premelting along the grain boundaries, which increases grain boundary mobility and consequently enhances SIBM.

Setting the temperature threshold for premelting
The in-situ temperature at which coarse and interlocking grains start to appear in polar ice sheets ( * about 262K) ( Table 1), 15 falls within the temperature range (258K to 263K) of the transition to a more temperature sensitive deformation mechanism during deformation tests (Mellor and Testa, 1969;Barnes et al., 1971;Weertman, 1983;Budd and Jacka, 1989;Paterson, 1994;Goldsby and Kohlstedt, 2001). The premelting temperature threshold for Glen's flow law (263K; Paterson, 1994) is 5K and 8K higher than the temperature thresholds for the dislocation creep (258K) mechanism and the GBS-limited creep mechanism (255K) applied by Goldsby and Kohlstedt (2001), respectively. Since the strain rate increase close to the melting point for 20 dislocation creep and GBS-limited creep has been related to premelting along the grain boundaries (Goldsby and Kohlstedt, 2001), a similar temperature threshold can be expected for both deformation mechanisms.
The temperature threshold of 258K proposed by Goldsby and Kohlstedt (2001) for dislocation creep was taken from Kirby et al. (1987), who conducted ice deformation tests at a high confining pressure of 50 MPa. A confining pressure of 50 MPa lowers the pressure-melting point by 3.7K, using the pressure-melting constant for clean ice of 7.410 −8 KPa −1 (Hobbs, 25 1974;Weertman, 1983;Equation 5). This change in pressure-melting point due to the high confining pressure seems not to be considered by Kirby et al. (1987) and Goldsby and Kohlstedt (2001). Therefore, it is argued that the corresponding temperature threshold should have been 261.7K instead of 258K, if a confining pressure of 50 MPa is also assumed. This temperature threshold is much closer to 263K used in Glen's flow law (Paterson, 1994) and practically equal to 262K that was found by analysing ice microstructures of polar ice cores (Table 1). 261.7K is also closer to the temperature threshold proposed by 30 Barnes et al. (1971), who found that the activation energy of ice is much higher between 271K and 265K (120 kJ mol -1 ) than between 265K and 259K (78.1 kJ mol -1 ). Similarly, 261.7K is also closer to Mellor and Testa (1969) and Budd and Jacka (1989) who found that above 263K the strain rate becomes progressively more temperature dependent when approaching the melting point.

Recrystallization and deformation mechanisms in the Eemian-glacial facies 35
The strain rate calculations using the composite flow law ( Figure 5) show that the fine grained layers in the Eemian-glacial facies deform predominantly by GBS-limited creep. It is known that the basal slip system is not significantly affected by the cryostatic pressures that are reached in polar ice sheets (e.g. Rigsby, 1958;Cole, 1996). Therefore, basal slip is an important strain producing mechanism in both the coarse and the fine grained layers, but the way basal slip is rate limited is different.
Since basal slip provides only two of five independent slip systems required for homogeneous deformation, at least one is favoured as the rate limiting mechanism for basal slip in the Eemian-glacial facies, since the grain boundary area in the impurity-rich and fine grained layers is relatively high and a higher grain boundary area enhances the effect of premelting on deformation behaviour (Barnes et al., 1971). However, compared to the glacial ice between 1419 m to 2207 m of depth ( Figure   2b), the grain boundary network in the fine grained layers in the Eemian-glacial facies is relatively irregular with many bulges (Figure 2a). The irregular grain boundary structure is likely a result of enhanced SIBM caused by premelting (Section 4.2). 5 The occurrence of SIBM implies there are differences in internal strain energy between grains that are related to the basal slip component of deformation, which is still significant even when GBS is the rate controlling process. Still, the effect of impurities in these impurity-rich layers is strong enough to prevent the grains from growing into tens of millimetres, like the example of the coarse grained ice core section in Figure 2b, so grain boundary sliding remains an important rate limiting mechanism. Due to the lower ratio of SIBM that is expected in these impurity-rich layers, the grains are longer-lived and can rotate towards a 10 single maximum CPO (e.g. Van der Veen and Whillans, 1994). For these layers, the CPO is a reflection of cumulative strain, just like the CPO in the shallower parts of the ice sheet (e.g. Azuma and Higashi, 1985;Alley, 1988;Budd and Jacka, 1989;Llorens et al., 2016aLlorens et al., , b, 2017. For the coarse grained layers in the Eemian-glacial facies the calculations using the chosen creep laws predicts that the deformation is not dominated by dislocation creep only, but that it has a substantial GBS-limited creep component going 15 up to 75% at 2485 m depth ( Figure 5). This would suggest that even in these coarse grained layers the creep behaviour is strongly grain size dependent. The question is whether this grain size dependence is in agreement with the interlocking grain boundary structure observed in the material (Figure 2b), since such a structure seems inconsistent with assumed sliding along grain boundaries. However, SIBM is highly active in these coarse grained layers and SIBM has been suggested to be a possible accomodation mechanism for basal slip (Pimienta and Duval, 1987;De la Chapelle et al., 1999 ;Duval et al., 2000;Montagnat 20 and Duval., 2000). If so, the flow law for GBS-limited creep is not applicable to these coarse grained materials. Alternatively, the original microstructure might have been obliterated by SIBM in situ. In that case, GBS might have locally rate limited basal slip (Raj and Ashby, 1971), hence basal slip might be rate limited by SIBM coupled by GBS (Drury et al., 1989), and the grain size dependent flow law (ε̇G BS ) might still be of relevance.
The grain size and grain shape in these low impurity interglacial layers (Figure 2b) suggests that the grain boundaries 25 are free to migrate at high SIBM rates (Duval and Castelnau, 1995;Schulson and Duval, 2009) which may be related to premelting (De la Chapelle et al. 1998) and are not or hardly influenced by impurities. The partial great circle to multi maxima CPO of these coarse grained ice core sections can be explained by the formation of new strain free grains with soft orientations (relatively high Schmid factor), which grow at the expense of grains oriented in a hard orientation (Alley, 1988;Durand et al., 2009;Montagnat et al., 2015;Qi et al., 2017). This recrystallization mechanism can be described as discontinuous migration 30 recrystallization (Wenk et al., 1989;Schulson andDuval, 2009) or SIBM-N (Faria et al., 2014a). The dominant deformation mode deep in the ice sheet is expected to be simple shear, yet the CPO maxima in the coarse grained ice suggests that deformation in these layers may involve dominant co-axial strain rather than simple shear.

Strain localization in the Eemian-glacial facies
The ice in the Eemian-glacial facies alternates between fine grained ice with a single maximum CPO and coarse grained ice 35 with a partial girdle CPO ( Figure 5). The differences in grain size, grain shape and CPO in the Eemian-glacial facies implies that there are large differences in viscosity between the different layers. This is also suggested by the results using the modified composite flow law ( Figure 5), that predict that the fine grained ice is much softer than the coarse grained ice when applying the modified composite flow law. Consequently, strain localization and strain partitioning into 'hard' and 'soft' layers can be expected. Strain localization has been shown on many different scales in ice (e.g. Paterson, 1991;Wilson and Zhang, 1996; CPO has, depending on it's orientation, a weakening effect on ice (e.g. Budd and Jacka, 1989;Faria et al., 2014b;Hudleston, 2015), so differences in CPO are likely to change the relative strain rates between the different ice layers shown in Figure 5.
Deformation experiments with ice from other polar ice cores with a certain type of CPO, such as a single maximum or a multi maxima CPO, have different strain rates when the ice is deformed under different deformation modes. For example, simple shear deformation experiments on basal ice with a multi maxima CPO from Law Dome showed that the strain rates were 5 comparable with those of isotropic ice (Russell-Head and Budd, 1979). The same study showed that samples from Law Dome with a single maximum CPO deformed much more readily than isotropic ice in simple shear (sheared in the direction of the measured surface velocity). The study of Lile (1978) with samples from Law Dome Summit and Cape Folger showed a similar result with samples containing a single maximum CPO that were deformed in simple shear (single maximum normal to the shear plane) showing much higher strain rates compared to laboratory-prepared isotropic ice with a similar grain size. For the 10 case of domiant simple shear, which is expected to be the deformation mode in this part of the NEEM ice core (Dansgaard and Johnsen, 1969;Montagnat et al., 2014), different CPOs in the fine and coarse layers could lead to even higher strain rate differences, than predicted in Figure 5 from the Goldsby and Kohlstedt 2001 flow laws. The composite flow law that is used in this study does not explicitely include the effect of CPO on strain rate, while it is well known that the CPO has a weakening effect on ice depending on its orientation in certain different deformation modes (e.g. Budd and Jacka, 1989;Faria et al., 15 2014b;Hudleston, 2015).
The difference in microstructure between the impurity-rich ice and the low impurity ice poses an interesting hypothesis for the effect of premelting on ice dynamics close to the bedrock. In the case of the deeper ice where premelt may occur, from here on called the 'premelting zone', consists entirely of interglacial ice (with a low impurity content) the premelting zone is 20 expected to be relatively viscous and hardly contributes to horizontal velocity, which will probably be localized above the premelting zone. In the case where glacial ice (with a high impurity content) is present in the premelting zone or the premelting zone consists entirely of glacial ice, a significant portion of the horizontal velocity will be accomplished in the premelting zone. The difference in microstructure of impurity-rich glacial and low impurity interglacial ice in the premelting zone can have important consequences for ice dynamics close to the bedrock. Since the impurity content in the Greenland ice sheet is 25 approximately 10 times higher than the impurity content in the Antarctic ice sheet (e.g. Legrand and Mayewski, 1997), this effect of strain partitioning in the premelting zone is likely to be stronger in the Greenland ice sheet than in the Antarctic ice sheet.
The hypothesis of the different effects of impurity-rich and low impurity ice on ice dynamics in the premelting zone close to the bedrock is supported by borehole logging data from several ice cores. Data from Byrd station showed that the 30 tilting rate (horizontal component of deformation rate) in the premelting zone (1810 m down to the bedrock at 2164 m of depth), where grains are coarse with a multi maxima CPO (Gow and Williamson, 1976), deformed much less than the remainder of the ice (Paterson, 1983). A similar observation for the EDML ice core was reported by . Morgan et al. (1997Morgan et al. ( , 1998 also reported that the tilting rate at Law Dome decreased with depth as grain size increased and CPO deviated from a single maximum CPO. In this case the decreasing strain rate has been explained by a decrease of stress, 35 caused by bed rock topography (Budd and Jacka, 1989). The highest simple shear strain rates over the entire depth profile in the Law dome (Dome Summit South) ice core, derived from the tilting, occur in a zone where the shear strain rates are otherwise decreasing. This layer is from the last glacial maximum and has a fine grain size and strong single maximum CPO.
The zone of high shear strain rate cannot be explained by variations in temperature or stress, but it can be explained by the combined influence of CPO and grain size. 40 We speculate that strain partitioning between glacial and interglacial layers in the premelting zone could lead to a different rate of layer thinning, which could have important consequences for interpreting paleoclimatic records from polar ice cores. In the deepest part of the ice core the dating is based on ice flow modelling describing a homogeneus transition from coaxial deformation to simple shear. It has often been shown that paleoclimatic records in the lower part of polar ice cores are disturbed (e.g. Alley et al., 1997;Gow et al., 1997;Suwa et al., 2006;Ruth et al.;NEEM community members, 2013), which could be caused by heterogeneous deformation and strain partitioning between glacial and interglacial layers as described above.

Conclusions 5
In many polar ice cores the grain size, grain shape and CPO change significantly in the ice close to the bedrock, which can have a large impact on the dominant deformation mechanism and the strain rate. Temperatures close to the bed rock are near the melting temperature and under these conditions enhanced creep and recrystallization can be explained by the occurrence of premelting along grain boundaries. In this study, actual temperature and grain size data of the NEEM ice core were used to apply the composite flow law of Goldsby and Kohlstedt (2001) and the Paterson (1994) version of Glen's flow law to the 10 lower part of the NEEM ice core with the aim of studying the effect of changes in grain size on the dominant deformation mechanism and the strain rate. Several stratigraphic disruptions are present in this part of the NEEM ice core, which causes layers of fine grained ice to be alternated by layers of coarse grained ice. After a microstructural evaluation of eight different polar ice cores from the Greenland and Antarctic ice sheets, it was found that microstructures that indicate premelting start at a temperature (T*) of about 262K, which is within the temperature range at which a more temperature sensitive deformation 15 mechanism starts to dominate the ice rheology in deformation tests. The composite flow law of Goldsby and Kohlstedt (2001) was modified to include this premelting temperature (T*) threshold of 262K.
The modified composite flow law predicts that, as a result of the grain size variation in the Eemian-glacial facies, the strain rate varies strongly with the fine grained layers deforming about an order of magnitude faster than the coarse grained layers. In the fine grained glacial ice the dominant deformation mechanism is predicted to be GBS-limited creep. In the coarse 20 grained interglacial ice, dislocation creep and GBS-limited creep contribute roughly equally to the bulk strain rate, with the contribution of GBS-limited creep to bulk strain rate increasing with depth. Glen's flow law, which is grain size insensitive, does not predict any variations in strain rate in the Eemian-glacial facies apart from a steadily increasing strain rate with depth caused by an increase in temperature with depth. Glen's flow law predicts a higher strain rate than the modified composite flow law along the entire lowest 540 m of depth of the NEEM ice core. The magnitude of the strain rate increase would be 25 stronger if a more realistic temperature dependence (e.g. Budd and Jacka 1989) for Glen's flow law is used.
Changes in grain size in the Eemian-glacial facies correlate strongly with changes in type and strength of CPO. The fine grained (<5 mm) impurity-rich glacial layers have a strong single maximum CPO, which is compatible with predominant simple shear deformation in this part of the NEEM ice core. The relatively fine grain size argues for GBS-limited creep to be the dominant deformation mechanism in these layers. The coarse grained (>5 mm) low impurity layers have a partial great 30 girdle to multi maxima type of CPO, which is more compatible with coaxial deformation than with simple shear deformation.
Due to the coarse grains and the interlocking grain boundary structure, these layers are likely deforming by basal slip rate limited by recovery via SIBM, which removes dislocations and stress concentrations in grains and allows further deformation to occur, or by coupled SIBM and grain boundary sliding. Therefore, strain partitioning is expected in the Eemian-glacial facies with the fine grained layers with a single maximum CPO deforming at high strain rates, while the coarse grained 35 interglacial layers with a partial girdle type of CPO deform at much lower strain rates. The difference in microstructure, and consequently difference in viscosity, of impurity-rich and low impurity ice in the premelting zone can have important consequences for ice dynamics close to the bedrock.

Acknowledgements
This work has been carried out as part of the Helmholtz Junior Research group "The effect of deformation mechanisms for ice sheet dynamics" (VH-NG-802). The NEEM light microscope data used in this study has been made available by www.pangaea.de. The authors would like to thank Sepp Kipfstuhl and Tobias Binder for providing data and encouraging discussions. David Prior and Adam Treverrow are thanked for elaborate and very helpful comments on the first versions of 5 the manuscript. The authors would like to thank all the NEEM Community members who were involved in the preparation of the physical properties samples in the field. This work is a contribution to the NEEM ice core project which is directed and    parameter. One class (green rectangle) has a fine mean grain size <5 mm and a first eigenvalue and Woodcock parameter that is comparable to the glacial ice and the other class (yellow rectangle) with a larger mean grain diameter (>5 mm) that has a lower eigenvalue and predominantly lower Woodcock parameter.  Table 1: Polar ice cores drilled at the Greenland and Antarctic ice sheets that show a sudden increase in grain size and change in CPO in the lower part of the ice core. The depth where these changes occur is given, together with ice core length, bottom borehole temperature, the in-situ temperature and the pressure-corrected temperature (T*) at the sudden grain size increase and change in CPO and the age of the ice at the transition to a sudden grain size increase and change in CPO. The age of the ice is given in marine isotope stages (MIS) and approximate ka BP (Lisiecki and Raymo, 2005 Table 3. A stress of 0.07 MPa and a mean grain diameter of 5 mm were used to calculate the strain rate. 5 Table 2: The flow law parameters of Glen's flow law (Paterson, 1994)

Creep regime A (units) n p Q (kJ mol -1 )
Glen's flow law (T<263K) 3.6110 5  (Paterson, 1994) and the members of the modified composite flow law for dislocation creep and GBS-limited creep of which some parameters remained the same as reported in Kohlstedt (1997, 2001). For this paper, the flow law parameters were contrained with the temperature threshold of 262K, which results in a change in activation energy and the pre-exponential factor for dislocation creep compared to the flow law used in our companion paper.