Cold ice within a polythermal ice body controls its flow dynamics through the temperature dependence of viscosity, and affects glacier hydrology by blocking water flow paths. Lakes on the surface, linked by persistent, deeply incised meltwater streams, are hallmark features of cold ice in the ablation zone of a glacier or ice sheet. Ice radar is a convenient method to map scattering from internal water bodies present in ice at the pressure melting temperature (PMT). Consequently, lack of internal scatters is indicative of cold ice. We use a helicopter-borne 30 MHz ice radar to delineate the extent of cold ice within Grenzgletscher (Zermatt, Swiss Alps). The inferred thermal structure is validated with temperature measurements in 15 deep boreholes, showing excellent agreement. The cold ice occupies 80–90 % of the total ice thickness in a 400 m wide flow band along the central flow line. Quantitative interpretation of ice radar scattering power indicates a decrease of ice water content between PMT and 0.5 K below PMT, as predicted by theory, and observed in the laboratory. The cold ice which emerges at the surface in the lower ablation zone is impermeable to water, and is thus devoid of moulins if not crevassed. The surface water from melt and rain is routed through deeply incised, persistent streams and lakes, and cryoconite holes are frequent, in stark contrast to the adjacent temperate ice from other tributaries. The cold ice thus has a strong control on glacier hydrology, but is likely to change due to continued warming.
 Ice sheets and many glaciers and small ice caps in the Arctic and Antarctic are polythermal, and therefore their thermal structure will likely change in a warming climate [e.g., Gusmeroli et al., 2012]. An ice body is called polythermal if zones of temperate ice at the pressure melting temperature (PMT) coexist with zones of cold ice (below the PMT) which are separated by the cold-temperate transition surface (CTS) [Blatter & Hutter, 1991]. The distribution of the thermal zones is controlled by a complex interplay between heat diffusion, heat advection by glacier flow, heat production by dissipation, water infiltration-refreezing processes in firn and ice zones, and warming by active moulins in the ablation zone [Phillips et al., 2010].
 Knowledge of the thermal structure of glaciers and ice sheets is crucial for modeling their future evolution, as temperature strongly influences ice viscosity, and therefore ice deformation patterns and mass flux [Hutter, 1983; Hutter et al., 1988; Blatter & Hutter, 1991]. In addition, zones of cold ice affect glacier hydrology by blocking meltwater fluxes, which are limited to discrete flow paths in cracks and channels [e.g., Jansson, 1996; Van der Veen, 1998; Boon & Sharp, 2003]. In contrast, temperate ice contains a network of intragranular veins where water flow is possible [Nye & Frank, 1973], if not blocked by air bubbles [Lliboutry, 1996]. Even if water fluxes in temperate ice are generally small, feedback effects may enlarge existing water flow paths, which tend to be preserved if water filled. Water-filled veins, cracks, or boreholes within cold ice usually refreeze within hours. Thus fracture-free cold ice is impermeable and facilitates the formation of persistent, deeply incised melt water streams and lakes at the glacier surface, which are indicators for cold ice [e.g., Hodgkins, 1997; Boon & Sharp, 2003]
 The Greenland ice sheet is cold in its central part, but exhibits temperate conditions at the base in extended zones along its margins [e.g., Greve, 1997] and even in some central parts with high geothermal heat flux [Dahl-Jensen et al., 1997]. The temperate ice reaches important thickness in fast flowing marginal areas [Lüthi et al., 2002] and is partly responsible for the fast flow of the major outlet glaciers [Iken et al., 1993; Funk et al., 1994b]. Polythermal Arctic glaciers and small ice caps often exhibit a more complex thermal structure [e.g., Blatter, 1987; Blatter & Kappenberger, 1988; Bamber, 1989; Pettersson et al., 2003; Gusmeroli et al., 2012] which is caused by the distribution of surface facies zones and the ice flow field [Aschwanden & Blatter, 2009]. In the Alps, the occurrence of cold ice is limited to glaciers with very high elevation accumulation zones [Haeberli, 1976; Suter et al., 2001; Eisen et al., 2009].
 Ice radar has been successfully used to map the extent of cold ice in polythermal ice masses. Water inclusions in the ice scatter the radar signals due to different dielectrical properties of ice and water [Hamran et al., 1996; Bamber, 1988; Bjørnsson et al., 1996]. Low-backscatter zones (LBZs) in ice radar signals correspond to cold ice with a negligible content of liquid water [Pettersson et al., 2003; Navarro et al., 2005], whereas strong scattering of radio waves has been interpreted as originating from liquid water inclusions in temperate ice [e.g., Bamber, 1988; Hamran et al., 1996] In addition to mapping the spatial extent, quantitative analysis of radar velocities and radar power have been used to infer ice water content [e.g., Murray et al., 2000; Pettersson et al., 2004; Gusmeroli et al., 2010]
 In this study we investigate the 3D-polythermal structure of Gorner-/Grenzgletscher (Zermatt, Switzerland) with helicopter-borne ice radar soundings and vertical temperature profiles from 15 boreholes. Cold ice extent is mapped by delineating LBZs, and a quantitative analysis of radar signal power is used to infer the liquid water content of the ice close to the CTS. The spatial extent of cold ice is set into relation with surface hydrology. This study is a sequel of [Eisen et al., 2009], in which the cold ice was mapped with a 40 MHz ground-based ice radar as zone of low backscatter. The LBZ occupied about 50 % of the total ice thickness in most profiles, considerably less than the cold ice determined with borehole temperature measurements (80–90% of ice thickness). This study presents a greatly extended set of englacial temperature data, and is based on a larger set of helicopter-borne radar data. From the two different data sets a similar extent of LBZ and cold ice was found.
2 Study Site
 The Gorner-/Grenzgletscher system of glaciers (Zermatt, Switzerland) covers an area of 60 km2 and spans an elevation range from 2200ma. s. l. at the terminus to an accumulation basin above 4000ma. s. l. (Figures 1 and 2). Ice temperatures between − 14.1∘C and − 12.5∘C throughout an ice column were measured on Colle Gnifetti at 4550ma. s. l. [Haeberli & Funk, 1991; Lüthi & Funk, 2001; Suter et al., 2001], which are presently rising due to atmospheric warming and meltwater infiltration [Hoelzle et al., 2011]. The coldest ice temperature measured in the ablation zone was − 2.8∘C (44m below surface) in 1975 [Haeberli, 1976], and is − 2.65∘C (70m below surface) at present [Eisen et al., 2009]. This cold ice occupies a flow band of 400 m width in the confluence area of Gornergletscher and Grenzgletscher [Eisen et al., 2009].
 In the confluence area, the ice marginal lake Gornersee forms every summer (outlines shown in Figure 10) which drains during an outburst flood in midsummer [Huss et al., 2007; Werder et al., 2009]. The lower Grenzgletscher branch (still named “Gornergletscher” on maps) has long been famous for its deeply incised, persistent meltwater streams and deep, blue lakes [Renaud, 1936].
3.1 Ice Temperature
 Ice temperatures were measured in 15 boreholes drilled in the summers 2004 to 2010 in the confluence area of Gornergletscher and Grenzgletscher (Figure 1). The holes were drilled with the VAW hot-water drill [Iken et al., 1989] close to bedrock (except holes f3 and ll5 where drilling progress stopped for unknown reasons). Boreholes drilled for sole purpose of temperature measurements were stopped above bedrock to preclude water circulation. An overview of the boreholes, including the depth, temperature characteristics and measurement method is given in Table 1.
Table 1. Locations and Characteristics of Boreholes Used to Determine the Thermal Structure of Grenzgletscher
Borehole designations in parentheses were used in [Eisen et al., 2009].
If hole did not reach the bed, the ice thickness was read from interpolated radar data.
Easting/Northing in the cartesian CH-1903 Swiss Coordinate System
The depth below surface of the CTS is given between the uppermost sensor at the PMT and the lowest cold sensor (Figure 3 and 4). Boreholes that are entirely temperate are marked with “temp.”
Measurement method: thermistor string measured with Fluke multimeter (TS); telemetry system (TM).
 Twelve boreholes were equipped with strings of thermistors, each consisting of nine NTC-thermistors (Fenwal 135-103FAG-J01) soldered onto a multicore cable, and sealed in metal tubes for stress relief. All thermistors were calibrated in a regulated calibration bath at four or five reference temperatures (± 20mK absolute accuracy) in the range of − 6∘C to 0∘C to determine individual temperature–resistivity relations. The absolute accuracy of measured temperatures is better than 50mK. The thermistor resistivities during calibration and after deployment were measured with the same digital Fluke multimeter in irregular time intervals.
 Upon completion of drilling with hot water, the temperature of cold ice in vicinity of the borehole is higher than its undisturbed value due to heat released during drilling and by refreezing of the borehole. A hyperbolic extrapolation [Humphrey & Echelmeyer, 1990] has been used to infer the undisturbed temperature (Appendix A).
 In three boreholes a telemetry system (improved version of the one used in Lüthi et al. [2002, Appendix A]) was installed to measure sensor inclination, orientation, water pressure and ice temperature. These temperature data had to be corrected for the heat released by the sensor electronics while powered during measurements. The temperature correction employed is described in Appendix B.
3.2 Ice Radar
 Airborne radar measurements were performed in February 2008 under dry-snow conditions to determine ice thickness and internal structures in the Gorner-/Grenzgletscher area. The data were collected with the University of Münster Airborne Ice Radar (UMAIR) [Blindow, 2009]. The system is designed to be used as a sling load from a helicopter which makes it suitable for smaller glaciers with steep surrounding terrain. The source pulse is a Ricker type wavelet at about 30 MHz center frequency stimulated by a 5kV pulser unit. The digital receiver has a 400 MHz sampling rate. Up to 10 measurements per second with 4096 samples each are made with 256-fold stacking. The positions of the antenna and the helicopter are recorded at 10Hz rate by dual frequency GPS receivers. Antenna altitude above ground is ideally 35m, and is recorded and displayed with a laser altimeter. At a helicopter flight velocity of 40kmh− 1 the distance between individual stacked traces is about 1m.
 Radar data processing comprised static corrections for topographic and flight altitude effects and bandpass filtering (15–100 MHz passband). The received radar signal power was amplified to correct for geometric spreading and damping losses using the radar equation [e.g., Ulaby et al., 1981],
where Ps is the signal power entering the ice at the surface, P the received power, R the range of a reflector below the glacier surface and α the attenuation factor. The scaling of Ps includes constant factors of antenna geometry and ice dielectricity. An attenuation factor of α = 0.0053m− 1(4.6dB/100m) is used throughout this paper. This value was determined in laboratory experiments at − 2.5∘C and a radar frequency of 35 MHz [Johari & Charette, 1975], and is consistent with values from Arctic glaciers [Bamber, 1987]. To convert two-way travel time to ice thickness, a radar signal velocity of 0.168mns− 1 for solid ice was used, which results in good agreement with borehole depths measured on Colle Gnifetti and Grenzgletscher [Lüthi & Funk, 2000; Eisen et al., 2009].
3.3 Ice Water Content
 Ice radar backscatter strength has been used to infer water content within a glacier [Bamber, 1988; Hamran et al., 1996; Pettersson et al., 2004; Macheret & Glazovsky, 2000]. The received radar signal power from scattering depends on size and spacing of liquid water inclusions within the ice body, as well as on details of coupling between antenna and ground. This problem can be circumvented by using the backscattered power relative to a reference of known water content [Hamran et al., 1996], which in our study is an englacial channel in 120 m depth below the surface. The volume fraction ω of liquid water in ice relative to a reference water content ωr of a scatterer at range Rr can then be determined with [Hamran et al., 1996]
where Pr is the reference signal power and P and R are received power and range of the scatterer. Equation ((2)) is strictly valid only at constant attenuation factor α, which might be altered by the presence of water in temperate ice [Pettersson et al., 2004; Navarro & Eisen, 2010]. In our case this limits the analysis to the layers in vicinity of the CTS as the upper boundary of temperate ice. Furthermore, α varies with temperature [Johari & Charette, 1975; MacGregor et al., 2007]. To obtain lower and upper bounds on water content, we performed the analysis with an additional attenuation factor corresponding to − 1.5∘C (α = 0.0057m− 1, 5dB/100m).
4.1 Ice Temperature
 Ice temperature was measured in 15 boreholes on Grenzgletscher at the locations indicated on Figure 1. Most holes were drilled along an approximate flow line (PF), and on two crossing profiles PX5 and PX9. Borehole designations are systematic along the central flow line (label “f”), with numbers indicating the approximate distance along the flow line in 100m intervals. Boreholes left of the central flow line (in flow direction) are labeled “l” and “ll”, those right of the flow line “r” and “rr”. Vertical profiles of ice temperature from six boreholes along the central flow line PF are shown in Figure 3. All profiles are similar in shape, with a thick layer of cold ice in the upper half, and some tens of meters of temperate ice at the bottom. Temperatures are increasing along the 1150m long flow line (f1, f3, f5, f9, f12, f13). The coldest temperatures between − 2.65∘C (hole f5) and − 2.1∘C (hole f13) are observed at depths of 75 to 45 m, with vertical position gradually rising along the flow line. Ice temperatures from four boreholes each located on the two across-flow profiles PX5 and PX9 are shown in Figure 4. Temperatures in the holes left or right of the flow line are markedly higher than on the central flow line (f5 resp. f9).
4.2 Temperate Ice
 Temperate ice (ice at the PMT) was detected at the bottom of all boreholes reaching the bed. Under the thickest cold ice the thickness of the temperate layer is about 30m, or ∼ 10 % of the ice thickness. To calculate the pressure melting temperature (PMT), the Clausius-Clapeyron equation of melting point depression was used. For pure ice the melting temperature Tm depends on absolute pressure p by
where Ttp = 273.16K and ptp = 611.73Pa are the triple point temperature and pressure of water. The Clausius-Clapeyron constant γ has been determined for pure water/ice as γp = 0.00742KMPa− 1, and for air saturated water as γa = 0.098KMPa− 1 [Harrison, 1975]. Overburden pressure p = ρigh at depth h is calculated with an experimentally determined ice density of 900kgm− 3 (data from Rüegg ) and g = 9.81ms− 2. The dashed lines representing the Tm in Figures 3 and 4 were calculated with γa (pure ice and air saturated water). Table 1 lists the range of the upper band of temperate ice between the lowermost cold sensor and the uppermost temperate sensor.
4.3 Extent of the Cold Ice
 The vertical and lateral extent of cold ice within Grenzgletscher can be best visualized in contour plots of ice temperature relative to the local PMT (Θ = T − Tm). Figures 5 and 6 show vertical sections along profiles PF and PX5. Clearly visible is a massive cold layer with coolest temperatures at 60 − 80m depth, and a temperate layer at the bottom. Along the flow line (Figure 5) the ice temperatures are gradually increasing in downstream direction, and the CTS is curving upward, indicating a thinning cold core and a thickening temperate basal layer. The contour plot of across-flow profile PX5 (Figure 6) shows that the cold ice is localized in a central flow band of 400m width, while the surrounding ice is temperate. Comparison with the map (Figure 1) reveals that the temperate areas are located under medial moraines, and therefore were in vicinity of valley walls in their upstream branches.
4.4 Ice Radar
 Roughly 35 km of helicopter-borne radar profiles were used in this study, covering the whole Gornergletscher/Grenzgletscher system from the terminus to the accumulation zone (profiles A to K, Figures 1 and 2). The signal quality is good, such that the bedrock reflection in depths of up to 450 m and internal structures are well resolved on all profiles. Common to all radar profiles are zones of high, uncorrelated scattering within the ice body. On all cross-sectional radar profiles of the lower glacier, extended zones of low backscatter are apparent. Radar profiles C and D (Figure 7) summarize these observations.
4.5 Low-Backscatter Zones
 Radar backscatter is sensitive to liquid water content. The diameter of water inclusions needed to act as individual scatterers depends on radar frequency, and is about 1/10 of the radar wavelength [Eisen et al., 2009]. To act as individual scatterers at 30 MHz, water inclusions would have to be larger than 0.5 m. It is more likely that a combined effect of many smaller scatters is observed. In general, low-backscatter zones (LBZs) in an ice radar profile indicate cold ice with a negligible liquid water content [Bjørnsson et al., 1996; Pettersson et al., 2003; Pettersson et al., 2004; Gusmeroli et al., 2012], whereas strong scattering of radio waves has been interpreted as originating from liquid water inclusions in temperate ice [e.g., Bamber, 1988; Hamran et al., 1996] The study by [Eisen et al., 2009] conclusively showed that areas with cold borehole temperatures on Grenzgletscher coincide with LBZs, although there was a considerable discrepancy in the vertical extent of cold ice. Figure 1 shows a map of the spatial distribution and thickness of the LBZ in our radar profiles.
 This thickness was automatically determined with an algorithm described in the Appendix C, or manually if near-surface scattering was too strong. The LBZ reaches a maximum thickness of 320m in the confluence area of Gorner- and Grenzgletscher (profiles A to F), and is between 50 to 100m thick in the upstream profiles (G to K). The side branch of Zwillingsgletscher also exhibits a central zone of low backscatter, which is separated from the Grenzgletscher LBZ by a region of high backscatter which coincides with a medial moraine. In contrast, the lower end of the Gornergletscher branch shows no indication of a LBZ. This agrees with results from drilling in that area during earlier campaigns where cold conditions can be ruled out as the boreholes did not refreeze during weeks [Iken et al., 1996].
 A quantitative inference of ice temperature from radar backscatter can be achieved by comparison of radar profile D to borehole temperatures of profile PX5 (closer than 30m). The contours of Θ = T − Tm in Figure 7 indicate that zones of high radar scatter coincide with ice temperature close to the PMT (Θ > − 0.25K), whereas scattering is almost absent in cold areas with Θ < − 0.5K.
4.6 Ice Water Content
 Received radar power from within the ice is an indicator of the density of scatters, which are assumed to be small bodies of liquid water within the ice [Hamran et al., 1996; Barrett et al., 2008]. Given a point of known water content as reference, the absolute water content can be determined with help of equation ((2)) [Pettersson et al., 2004]. Such a backscatter reference is visible in radar profile D (arrow in Figure 8) in form of a water-filled englacial water channel at 130m depth. This englacial channel was encountered during drilling of hole r6, when borehole water level dropped rapidly upon reaching 120m depth. For further analysis we interpret this feature as an active englacial channel with 100 % water content.
 Figure 8 shows the inferred water content ω on radar profile D, as calculated with equation ((2)). There is a striking coincidence between low water content and cold ice temperature, whereas ice of high water content is localized under the medial moraines. Bright spots close to the glacier bed might indicate water-filled branches of the subglacial drainage system.
 The relationship between received radar power and ice temperature can be quantitatively investigated in several boreholes that are located in close vicinity of radar profiles. Figure 9a shows the temperature profiles of boreholes f5 and l5 (within 30 m distance from radar profile D), and f1 (within 20 m of radar profile E). For each borehole, radar signal power from the three closest radar traces was averaged, and the water content was calculated using equation ((2)). The ice water content calculated for the three boreholes is shown in Figure 9c, and for each individual temperature sensor in Figure 9b. The water content in vicinity of boreholes f1 and f5 is below 0.1 % where the temperature is lower than 0.5K below PMT. In borehole l5 the amount of scatterers, and therefore the inferred water content, is higher (0.2 % to 0.8 %) at several depths. One such peak coincides with the kink in the temperature profile at 160m (Figure 9a). The origin of these scatterers is unknown, but might be attributable to englacial water seeping through small vertical cracks which are frequent in the confluence area.
5.1 Cold Ice Body
 The shape of all cold temperature profiles (Figures 3 and 4) is typical for a regime dominated by heat advection, and resembles temperature profiles measured in fast flowing polar glaciers [e.g., Blotter, 1987] and the Greenland ice sheet [e.g., Funk et al., 1994a; Lüthi et al., 2002] Like in polar glaciers and ice sheets, the thick body of cold ice in the ablation area of Grenzgletscher is an advected feature. The cold ice originates from the high altitude accumulation zone above 4000 m a.s.l. (shaded in pink in Figure 1, [Suter & Hoelzle, 2002] with coldest temperatures of − 14.1∘C measured on Colle Gnifetti [Lüthi & Funk, 2001] Conversion of potential energy to heat by dissipation would raise temperature by 9.5K during a 2000 m drop. As the ice in the upper half of an ice body barely deforms, most of this energy is released close to the bed which explains temperate conditions there. Also, it seems reasonable to assume that a considerable amount of ice is melted at the base, which constitutes a continuous source of subglacial meltwater.
 The core of cold ice in the center of Grenzgletscher occupies 90 % of the ice thickness at the upstream end of the flow line PF, and diminishes to about 70 % at the downstream end (Figure 5). The temperature minimum of the cold ice body along the central flow line PF rises by 0.5K between boreholes f1 and f13. Figure 3 shows that this temperature increase is almost uniform along a vertical profile. The considerable vertical and lateral heat fluxes are sufficient to explain this warming. The vertical heat flux toward the coldest zone is driven by vertical temperature gradients between 12 and 20mKm− 1, corresponding to 24 to 42mWm− 2 heat flux (calculated with a thermal conductivity k = 2.1Wm− 1K− 1; [Paterson, 1999] Lateral temperature gradients are of the order of 10mKm− 1 at 100m depth, corresponding to a horizontal heat flux of 20mWm− 2. At an average flow velocity of 30ma− 1 the transit time between f1 and f13 is about 40 years. Calculating the conductive heat flux into a cylinder of 50–100 m radius during 40 years leads to 0.3 to 0.7K increase of the temperature within the cylinder. Therefore, it is likely that the temperature increase is mainly due to heat conduction, as dissipative heat production is small at the low deformation rates in the upper half of the glacier. Detailed thermo-mechanical modeling is underway to investigate whether the observed temperature distribution is stationary, or is affected by rising surface temperatures and a transient flow field.
 Some peculiarities in the ice temperature profiles are discussed next. Borehole f3 is slightly warmer than the downstream borehole f5 (Figure 3). Since borehole f3 is not strictly located on the central flow line, but 30m South, this temperature difference is an expression of the considerable horizontal temperature gradients, which are visible in Figure 6.
 The temperature profile of borehole l9b (Figure 4) is 1.5K warmer than the nearby borehole l9a. Radar profile C (Figure 7) shows a zone of high backscatter below 100 m depth in the center of the 400 m wide LBZ around borehole l9b. A possible explanation for this backscatter anomaly is heat release from a former moulin. After drilling (in 2010) a small moulin formed in 10m distance from the borehole. Since the radar profiles were acquired in 2008 under dry-snow conditions, the reflecting feature cannot be caused by this moulin or by the borehole, but indicates a hydrologic feature that has persisted within the otherwise cold ice body, and which was reactivated in 2010. Similar signatures have been observed in the marginal zone of the Greenland ice sheet. Waveform modeling showed that they are likely produced by water-filled cavities or channels [Catania et al., 2008]. If so, the presence of moving water would heat the cold ice considerably, as was observed in borehole l9b, and would be an example of the cryo-hydrological warming proposed for cold ice [Phillips et al., 2010].
5.2 Low-Backscatter Zones
 Low-backscatter zones (LBZ) are observed in all radar profiles crossing the Grenzgletscher branch. They are also visible in the Zwillingsgletscher side branch, while they are absent in Gornergletscher (Figure 1). The LBZs extend from the highest accumulation zone with cold ice and internal layering [Lüthi, 1999] to the glacier terminus, and are especially pronounced in the confluence area where they occupy up to 90% of the ice thickness of 300–400 m.
 Low-backscatter zones of similar spatial extent have been detected in earlier, ground-based radar measurements with 40 MHz center frequency [Eisen et al., 2009]. The lower boundary of those LBZs, termed the “radar transition surface” (RTS), was consistently at a shallower depth than the CTS. The vertical extent and therefore the amount of cold ice was considerably underestimated. This difference might be partly attributable to a different signal to noise ratio, which was greatly enhanced in the helicopter-borne measurements with more signal stacking (256-fold instead of 8-fold) and a much higher capacity regarding the antenna gain. Furthermore, signal quality of ground-based radar on an undulating surface is degraded by a varying antenna geometry, a source of noise not present with the constant antenna geometry of the helicopter-borne UMAIR system.
5.3 Ice Water Content
 We inferred the ice water content by comparing scattered signal power to a known reference scatterer of 100% water content (englacial channel in Figure 8). Quantitative analysis in Figure 9b shows that the ice water content increases in a systematic manner toward the PMT (Θ = T − Tm = 0K) for all three boreholes. According to theory and laboratory experiments, the relation between the diameter a of water veins in cold ice and temperature is Θ = Ca− 1.82 [Mader, 1992b]. Interstitial water volume between ice grains will then be proportional to the square of the vein diameter a. The ice water content therefore is
where C′ is a constant that depends on the density of intracrystalline veins, and therefore ice density [Lliboutry, 1996], and on the soluble impurity concentration in the water. The curves in Figure 9b correspond to equation ((4)) with C′ = 0.05 (dash-dotted) as upper bound and C′ = 0.01 (dashed) as lower bound. The respective values of C are in the range 15 to 65, and therefore of the same order as Mader's value of 25. The agreement corroborates that the findings of laboratory experiments [Mader, 1992a, 1992b] are transferable to in situ conditions in a polythermal glacier. This result is significant since it implies that the CTS is a zone of increasing water content as the PMT is approached, rather than a singular phase transition surface.
 For each of the three boreholes the inferred water content in Figure 9c increases strongly in the depth range where the CTS is located according to the temperature measurements (Table 1). In each location, two peaks in water content are found in vicinity of the CTS: 0.8 % and 2.8 % at 266 m and 274 m depth in borehole f1 (red); 0.55 % and 3.2 % at 292 m and 298 m depth in borehole f5 (blue); 0.95 % and 2.5 % at 292 m and 311 m depth in borehole l5 (green). These inferred water contents depend strongly on the assumed attenuation factor α. For example, using a value for − 1.5∘C instead − 2.5∘C (0.0057 instead of 0.0053) increases the inferred water content by 30%. Therefore, we regard the above values as lower limits, especially for the relatively warm ice at borehole l5. Comparing our inferred water contents at the CTS to other studies shows that our lower values (first peaks) are similar: [Pettersson et al., 2004] found values between 0.58 % and 0.79 %, and [Gusmeroli et al., 2010] found 0.6 %. Our higher values (second peaks) are in the range found on other glaciers (summarized in Table 1 of [Pettersson et al., 2004] Even higher values up to 9 % were inferred in one study [Macheret & Glazovsky, 2000]. The rather high values of inferred water content we find below the CTS (i.e., more than 10 % for borehole f1) might be the result of macroscopic water volumes like water-filled crevasses or channels.
5.4 Consequences for Glacier Dynamics
 Glacier dynamics is affected by cold ice through the dependence of ice viscosity on temperature. Viscosity at a temperature of − 2∘C is about twice that of temperate ice [e.g., Cuffey & Paterson, 2010] Since cold ice occupies between 70 and 90 % of the ice thickness in the central part of Grenzgletscher, it is likely to affect the ice flow pattern in the whole confluence area. Longitudinal stress transfer through the cold ice from the steep zone (in vicinity of profiles F and G) will tend to push the ice toward North, and partially block ice flow from Gornergletscher. As a consequence, one would expect that measured flow velocities cannot be reproduced with an ice flow model employing the flow law of temperate ice. Indeed, even by varying basal sliding motion in a isothermal 3D full-Stokes ice flow model, an agreement between modeled and measured flow velocities could not be obtained [Riesen et al., 2010].
5.5 Consequences for Glacier Hydrology
 Cold ice is impermeable to meltwater, except for water forcing its way by hydrofracturing [Van der Veen, 1998], or for water flowing permanently through cracks or channels [Boon & Sharp, 2003]. Stagnant water within cold ice freezes within days even at the moderately cold temperature of − 2∘C, as was observed in the cold sections of the boreholes described above (Figure 11).
 The cold ice detected in the boreholes is gradually exposed at the surface downstream of our drill sites, as melting removes ice from the surface. The impermeability of this cold ice leads to surface morphological features which are prominently visible in the foreground of Figure 2. Lakes of more than 20 m diameter form on the glacier surface, and meltwater streams flow through deeply (10–30 m) incised, meandering canyons that persist for many years. This kind of hydrological features, often observed in Arctic polythermal glaciers, is unique in the Alps. They were the topic of a detailed monograph [Renaud, 1936], and are even indicated on topographic maps. It is important to emphasize that such deeply incised streams and big surficial lakes are absent on the adjacent temperate Gornergletscher branch (left confluence in Figure 2), and also at the margins of the Grenzgletscher branch where the ice is temperate (Figure 7).
 The locations of persistent, deeply incised hydrological features at the glacier surface (mapped from 2006 aerial photography and during the 2006/07 field seasons by [Rüegg, 2007] are compared to the extent of the cold ice in Figure 10. Lakes and the deeply incised meltwater channels coincide with areas where cold ice was mapped with radar. There is also a striking coincidence of almost moulin-free zones within the cold ice, whereas the density of moulins is high in the adjacent temperate ice. The only cold area of high moulin density is found within the crevassed zone, which is caused by extensional stresses as the ice flow changes direction. A few moulins persist in the center of the cold ice downstream of the crevassed zone, which were likely advected from the crevassed zone where they formed. Such moulins have to carry important meltwater fluxes to warm the surrounding ice sufficiently, such that refreezing is not complete when water supply stops during winter. The warmer ice found in borehole l9b, and the observed radar scatterers in that area, are likely due to this process.
 The ice marginal lake Gornersee forms every summer in the confluence of Gorner- and Grenzgletscher (outlines are shown in Figure 10), and drains between 4 and 6 × 106m3 water within several days during an outburst flood in midsummer [Huss et al., 2007]. Different modes of drainage have been observed in the summers of 2004 to 2008: subglacial, englacial through a big channel, and superficial through a progressively incised gorge with a final depth of 50m [Werder et al., 2009]. To what extent the thick, cold ice is responsible for damming of the lake is difficult to assess. It is likely that the cold ice precludes drainage through the main body of the glacier, such that englacial drainage pathways are restricted to the temperate ice close to the bed, and along the medial moraine formed by Gorner- and Grenzgletscher [Huss et al., 2007; Sugiyama et al., 2008].
5.6 Consequences for Glacier Mass Balance
 The cold ice advected from the accumulation zone above 4000 m a.s.l. moves through a temperate accumulation zone where it is buried by temperate firn/ice [Suter et al., 2001]. This temperate ice is subsequently removed by ablation, until in the confluence zone the central core of cold ice is emerging at the surface. There is strong visual indication of this process, as the morphology of the glacier surface changes along the flow line. In vicinity of boreholes f1, f3, and f5 (Figure 1) the ice is dusty and exposes different shades of gray, while cryoconite holes are infrequent or absent. Dust blown from the adjacent exposed moraines is likely the main source of this color. Around boreholes f12 and f13 and further downstream, the surface appears in bright white, and water-filled cryoconite holes are abundant. The ice in that area is exceptionally slippery, even on a hot summer day. These empirical indications of cold ice outcropping in the lower ablation zone (below borehole f12) are supported by exceptionally bright appearance of that zone on aerial photography and satellite imagery (Landsat 7 ETM+, channel 2), which is limited to the cold Grenzgletscher branch.
 Cold ice, through its high content in air bubbles and low content in liquid water, reflects incoming radiation and has a high albedo [Warren & Brandt, 2008]. Ablation is therefore considerably reduced as compared to temperate ice, where liquid water in veins absorbs radiation. The ubiquitous presence of dust particles further reduces albedo and thus increases ablation. Preliminary comparison of ablation measurements from stakes with surface albedo and ice temperatures corroborates the above propositions and will be the topic of a further study.
 A possible mechanism explaining the observation that dusty surface ice is becoming clear as it moves in the lower ablation area is the formation of cryoconite holes [MacDonell & Fitzsimons, 2008]. In temperate ice, melt water seeps through the surface, which is often rotten by radiation, leaving the insoluble dust particles at the surface. In contrast, cold ice is impermeable to water, which runs over the surface, and collects in depressions. Dust particles are thus moved along with the water to depressions where they assemble. These collections of particles absorb heat, locally increasing melt, and thus forming cryoconite holes [Bøggild et al., 2010].
 Outcropping of cold ice at the glacier surface in the lower ablation zone has the effect of concentrating dust particles in cryoconite holes, thus brightening the surface and reducing albedo. This process might explain the presence of a dark zone in the upper ablation area of the Greenland ice sheet [Wientjes & Oerlemans, 2010; Wientjes et al., 2011], while the downstream ablation area is bright and clear.
 We used a combination of ice temperature measurements in 15 deep boreholes together with helicopter-borne ice radar to delineate the polythermal structure of Grenzgletscher. These methods are complementary: Borehole measurements provide absolute temperature with high accuracy, whereas ice radar provides a glacier-wide picture of the distribution of temperate and cold ice. Our measurements show that the cold ice is located within a narrow central core that is advected from a very high accumulation area. The cold ice occupies up to 90 % of the ice thickness within a 400m wide flow band in the confluence area with Gornergletscher, and extends to the glacier terminus where it is gradually exposed at the surface by ablation. The ice is coldest along the central flow line in 60 − 80m depth, and gradually rising downstream. Surface brightening through the outcropping of cold ice in the lower ablation zone presumably is an important process affecting glacier mass balance.
 Absolute ice water content was inferred from returned radar power by comparison with a reflector assumed to be a water-filled englacial channel. We inferred that interstitial water volume within the ice matrix increases from virtually none at a temperature colder than 0.5K below PMT to about 0.5 − 1 % at PMT. This increase follows the functional relationship determined in laboratory experiments. The inferred water content within the temperate ice varies but is in the order of a few percent. Also higher values of more than 10 % are found, however these might be due to the presence of a channel. Much higher values in vicinity of the bedrock are most likely related to subglacial drainage pathways in a localized or distributed hydrological system [Harper et al., 2010]. The polythermal structure of Grenzgletscher has a strong influence on its flow dynamics and hydrology. Due to the strong dependence of ice viscosity on temperature, and on ice water content, thermo-mechanically coupled ice flow models are required to assess their flow dynamics [Aschwanden & Blatter, 2009].
 The close agreement of cold ice zones with surface hydrological features such as meltwater lakes, persistent deeply incised meltwater streams, and the near-absence of moulins shows, that these features can be used as indicators of the presence of cold ice [Hodgkins, 1997; Boon & Sharp, 2003]. These findings might be used for the remote detection of changes of the thermal structure of Arctic glaciers and the marginal zones of Greenland and Antarctic ice sheets: Changes of the distribution of surficial lakes and meltwater streams could be used to indicate thermal changes within the ice body, which in turn affect ice dynamics.
 It is likely that the annual formation of ice-dammed Gornersee, its volume and drainage mode is controlled by the presence of cold, impermeable ice. Thus, the presence of cold ice might play an important role understanding and predicting glacier lake outburst floods, especially in mountain ranges with very high accumulation areas.
 The results presented in this study are similar to many findings observed under Arctic and Antarctic conditions. The thermal and surface hydrological characteristics of Grenzgletscher are due to the same processes controlling Arctic glaciers and the marginal zones of the Greenland and Antarctic ice sheets. A better understanding of polythermal Alpine glaciers therefore could advance the understanding of processes controlling the evolution of Greenland and Antarctica, but at a much reduced logistical effort.
 Upon completion of drilling with hot water, the temperature of cold ice in vicinity of the borehole is raised with respect to its undisturbed value due to heat released during drilling and by refreezing of the borehole. Figure 11 shows a typical example of the temperature evolution at an individual temperature sensor. Initial cooling is slow for several days until the borehole is completely refrozen. After a phase of rapid cooling, the temperature asymptotically approaches the undisturbed ice temperature T0 within several months. The value of T0 was calculated from the first ten days of measurements with an extrapolation procedure. For this purpose the borehole was considered as an instantaneous line source of heat. The temperature T(t) in the borehole center then evolves according to [Humphrey & Echelmeyer, 1990], Eq. 24)
where T0 is the undisturbed ice temperature, Q the heat released per unit length of the borehole, k the heat conductivity of ice, and t is time. The delay s until the onset of asymptotic cooling (equilibration phase in Figure 11) had to be introduced in addition to Formula (24) in [Humphrey & Echelmeyer, 1990].
 The quantities T0, Q and s were determined for each temperature sensor by fitting equation ((5)) to the temperatures measured during the equilibration phase. The extrapolated temperature T0 is within 30 mK of the temperature measured three month after drilling.
Correction of Telemetry System Data
 To reduce power consumption of the telemetry system, the measurement interval of 2 minutes in summer was reduced to 15 minutes during winter. This interval change allows for correction of the heat released by the sensor electronics. Assuming steady temperature and radial heat flow, the total heating power of the sensor unit is related to ice temperature as [Carslaw and Jaeger, 1959, chapter 9.1]
where is the temperature measured at sensor unit, rc the radius of sensor unit, T0 the undisturbed ice temperature and k the conductivity of ice.
 Changing the measurement interval leads to different heat release rates in the sensor: (measuring every 120 s in summer) and (measuring every 15 minutes in winter), with corresponding temperatures T120 and T900. Assuming that the change in measurement interval is proportional to the change in heat release (i.e., constant heat release rate during operation), leads to the relation
and solving for the undisturbed ice temperature
 The largest difference from the measured temperatures during the winter interval to the calculated undisturbed temperatures was 0.017 K, which is smaller than the accuracy of the single thermistor. However, the differences of the undisturbed temperatures to the temperatures measured in the summer interval were as high as 0.13 K.
Automatic Detection of Extent of Low-Backscatter Zone (LBZ)
 A simple algorithm to automatically detect the extent of the LBZ was implemented. Assuming that random scatterers are homogeneously distributed within the cold ice and have equal scattering cross section, the reflected power of the radar signal (corrected with equation (1)) should increase with R2 (the scatterers are located on the surface of a sphere [Hamran et al., 1996] To make the algorithm insensitive to random scatterers, we use the cumulative signal strength which varies like R3.
 At the depth where the cumulative signal strength exceeds the value expected for random scatterers, additional scatterers, such as more or larger water inclusions, are located. This is the depth where the transition from cold to temperate ice (i.e., the CTS) is expected.
 A somewhat arbitrary threshold of twice the theoretical signal strength was used to determine the lower boundary of the LBZ in each radar trace (indicated with red bars in Figure 12). This threshold proved to be useful since signal strength increases considerably at this value in all traces. Comparison with temperature measurements shows that the lower boundary of the thus determined LBZ lies in the range where the CTS is located. The location of the CTS is only known within a few meters (Table 1) which is also the accuracy of this method. The described method was applied to all radar traces, and mostly provided satisfactory results. Radar profiles I, J and K are located within the crevasse-rich lower accumulation zone with strong reflectors close to the surface which preclude automatic detection. In these profiles the LBZ was picked manually.
 We thank P. Riesen, M. Werder and everybody involved in the field work. Sensor electronics and mechanical manufacturing was supported by C. Senn, K. Schroff and T. Wyder. O. Eisen, M. Huss and H. Blatter commented on earlier versions of the manuscript. We acknowledge the thoughtful reviews of Alessio Gusmeroli and two anonymous reviewers. The Swiss Army provided knives and helicopter support, and the International Foundation High Altitude Research Stations Jungfraujoch and Gornergrat (HFSJG) supported personnel transport. This work was funded by the Swiss National Science Foundation grants 200020-111892 and 200021-127197.