Vertical distribution of water within the polythermal Storglaciären, Sweden

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115,, doi: /2009jf001539, 2010 Vertical distribution of water within the polythermal Storglaciären, Sweden Alessio Gusmeroli, 1,2 Tavi Murray, 1 Peter Jansson, 3 Rickard Pettersson, 4 Andy Aschwanden, 5 and Adam D. Booth 1 Received 24 September 2009; revised 29 May 2010; accepted 7 June 2010; published 5 October [1] Knowledge of water content and its distribution in polythermal glaciers is required to model their flow and thermal state. However, observations of water content variations with depth in polythermal glaciers are scarce. Water content can be estimated from radio wave speed because they depend on one another. We obtained continuous profiles of radio wave speed variations with depth from zero offset radar profiles collected in boreholes approximately 80 m deep in the upper ablation area of Storglaciären, northern Sweden. These profiles show that the microcrystalline water system in the temperate ice is relatively homogeneous. The overall hydrothermal structure at this location is composed of a 20 m thick upper layer of cold, water free ice, underlain by a temperate ice layer whose average water content is 0.6% ± 0.3%. These results are corroborated by surface radar and thermistor measurements, which show that the depth of the cold temperate transition is 21 m and the calculated water content at that transition is 0.6% ± 0.1%. These findings imply that the whole temperate ice layer is from 3 to 4 times softer than the cold ice and, consequently, that realistic ice flow models of polythermal glaciers should include the effect of water content on viscosity. Citation: Gusmeroli, A., T. Murray, P. Jansson, R. Pettersson, A. Aschwanden, and A. D. Booth (2010), Vertical distribution of water within the polythermal Storglaciären, Sweden, J. Geophys. Res., 115,, doi: /2009jf Introduction [2] Understanding the spatial distribution and the amount of liquid water within glaciers is essential because the flow and thermal behavior of ice masses are directly linked to the ways in which water occurs within them [Duval, 1977; Fountain and Walder, 1998; Zwally et al., 2002; Jansson et al., 2003; Fountain et al., 2005]. Liquid water, generated from melting snow or direct input from rainfall, is routed downglacier by supraglacial streams. When such streams intersect vertical shafts (moulins), crevasses, or fractures, water can enter the macroscopic englacial water system ((MWS) Figure 1a) mainly composed of a network of decimeter size, hydraulically connected fractures which can route significant volumes of water to the bed of the glacier [Fountain and Walder, 1998; Fountain et al., 2005]. [3] Water in glaciers also occurs in a fundamentally different system disconnected from the MWS: the microscopic water system ((mws) Figure 1b). The mws consists of 1 Department of Geography, Glaciology Group, Swansea University, Swansea, UK. 2 Now at Department of Geology and Geophysics, University of Alaska Fairbanks, Fairbanks, Alaska, USA. 3 Department of Physical Geography and Quaternary Geology, Stockholm University, Stockholm, Sweden. 4 Department of Earth Sciences, Uppsala University, Uppsala, Sweden. 5 Arctic Region Supercomputing Center, University of Alaska Fairbanks, Fairbanks, Alaska, USA. Copyright 2010 by the American Geophysical Union /10/2009JF (mm scale) water inclusions found in veins and nodes along three grain intersections, in lenses on grain boundaries, and in irregular shapes [Raymond and Harrison, 1975; Nye, 1989; Mader, 1992; Fountain and Walder, 1998]. Such water inclusions are primarily generated in the accumulation area, where meltwater percolates through the porous firn and becomes part of the glacier ice crystalline structure when the pores close by compaction [Paterson, 1971; Lliboutry, 1976; Pettersson et al., 2004]. [4] The mws is primarily controlled by ice temperature [Paterson, 1994] and is only present in those glaciers where the temperature reaches the pressure melting point. When the entire glacier is at the pressure melting point, the glacier is temperate, whereas when some regions of the glacier are below freezing (cold, Figure 1c) and others are at the melting point (temperate), the glacier is polythermal (Figure 1) [Hutter et al., 1988; Paterson, 1994]. Recently, Aschwanden and Blatter [2009] treated glacier ice in polythermal glaciers as a continuous system dominated by enthalpy: ice is defined as cold if a change in enthalpy leads to a change in temperature alone, whereas it is defined as temperate if such change leads to a change in water content in the mws alone. The englacial phase boundary, which separates cold and temperate ice in polythermal glaciers, is the cold temperate transition surface (CTS) (Figure 1a) [Hutter et al., 1988; Pettersson et al., 2003]: across this boundary, water content in the mws rises from zero to positive volumetric percentages. [5] Considerable research has focused on defining the theoretical principles and undertaking numerical modeling 1of14

2 Figure 1. (a)sketchofastorglaciären like polythermal glacier with indication of terminology used in this paper. The macroscopic englacial water system (MWS) is indicated by the dashed arrows. (b) Temperate ice with the microscopic water system (mws). (c) Cold ice with no water. The cold temperate transition surface (CTS) is the englacial boundary which separates temperate ice (Figure 1b) from the cold ice (Figure 1c). of polythermal glaciers [Fowler and Larson, 1978; Fowler, 1984; Hutter et al., 1988; Blatter and Hutter, 1991; Aschwanden and Blatter, 2005, 2009]. In such models, it is essential to know the temperature and water content distribution since they both strongly affect ice viscosity [Glen, 1955; Duval, 1977]. The softness parameter A (also known as the rate factor) varies with temperature T and volumetric water fraction w according to AðT; w Þ¼A 0 ð w Þ expð Q=RTÞ; ð1þ where A 0 ( w ) is a temperature independent, water contentdependent rate factor [Duval, 1977; Paterson, 1994], and Q and R are the activation energy for creep in ice (139 kj mol 1 for T > 10 C [Paterson, 1994]) and the universal gas constant (8.134 J mol 1 K), respectively. [6] Equation (1) shows that accurate quantification of both T and w is required to predict the mechanical behavior of polythermal glaciers. Despite this fact, there is a lack of data providing detailed experimental evidence of simultaneous measurements of temperature and water content distributions in polythermal glaciers. Many workers have reported temperature profiles with depth for polythermal glaciers in Scandinavia [Hooke et al., 1983], Canadian Arctic [Blatter and Kappenberger, 1988], China [Maohuan, 1990], and Svalbard [Björnsson et al., 1996], but we are aware of only two polythermal glaciers in which temperature and water content estimates (published with measurement error) have been compared: Bakaninbreen in Svalbard [Murray et al., 2000a, 2007] and Storglaciären in northern Sweden [Pettersson et al., 2004]. These studies reported temperature profiles within the ice column but only gave bulk estimates of w for the temperate ice. In particular, Murray et al. [2000a, 2007] obtained a bulk average, w = 1.29% (+1.68, 1.14), for the whole 40 m thick temperate layer of Bakaninbreen, and Pettersson et al. [2004] estimated average w = 0.8% ± 0.3% at the CTS of Storglaciären. It is therefore clear that there is a very limited knowledge on how water content in mws varies with depth in polythermal glaciers. [7] Current understanding of the spatial distribution of water content within glaciers comes largely from geophysical investigations because changes in the propagation speed and attenuation of radio and seismic waves can be related to variations in the water content of glaciers [e.g., Looyenga, 1965; Paren, 1970; Bradford and Harper, 2005; Endres et al., 2009]. The strong dielectric contrast between glacier ice and liquid water makes radio wave speed profiling particularly efficient when describing the hydrothermal state of ice masses. Speeds higher than m ns 1 are typical of dry, water free ice, while lower speeds are typical of ice which contains some volumetric percentage of liquid water [Macheret et al., 1993; Murray et al., 2000b; Bradford and Harper, 2005]. However, the presence of air in wet ice can complicate this interpretation [Bradford and Harper, 2005; Gusmeroli et al., 2008]. [8] In this study we investigate vertical variations of water content in the mws of the polythermal Storglaciären, northern Sweden, using detailed radio wave speed profiles obtained by borehole radar zero offset profiling (ZOP) [Peterson, 2001; Binley et al., 2001; Huisman et al., 2003]. The ice thickness and thermal state of the study area were determined using common offset (CO) ground penetrating radar (GPR) data and thermistor strings. We then assess our water content profiles by investigating the presence of critically refracted raypaths [Rucker and Ferré, 2004; West and Truss, 2006] and by forward modeling the effect that water features in the MWS can have on radio wave speed estimates. We finally estimate the implications that such water contents have on ice viscosity using equation (1) and experimental results by Duval [1977]. 2. Storglaciären [9] Storglaciären is a small polythermal valley glacier located on the eastern side of the Kebnekaise massif in Lapland, Arctic Sweden (Figure 2). In this region, the melting season typically starts in June, reaches its peak in July, and terminates at the end of September. The polythermal structure of the glacier has been mapped using direct temperature measurements [Schytt, 1968; Hooke et al., 1983] and GPR [Holmlund and Eriksson, 1989; Pettersson et al., 2003]. The glacier is temperate in most parts ( 85%), except for a cold surface layer in the ablation area. The cold layer is thickest at the terminus and at the margins (maximum thickness 60 m), while it is thinnest toward the center of the glacier and toward the equilibrium line (Figure 1 depicts a similar polythermal structure). The glacier is frozen to the bed close to its margins, over 16% of its area [Holmlund et al., 1996]. [10] The water content at the cold temperate transition surface is typically low, less than 1% in an area close to the equilibrium line [Pettersson et al., 2004]. Spatial variations in water content at the CTS have also been observed, showing a distinct pattern with higher values on the northern side of the glacier [Pettersson et al., 2004]. This variability is believed to be a consequence of ice originating from two different cirques with different properties [Pettersson et al., 2004]. Observations of the hydraulic state of Storglaciären are, however, limited to the depth of the CTS. How water content changes with depth is still unknown. Aschwanden and Blatter [2005] quantified the meltwater production because of strain heating along the kinematic center line of the glacier; they predicted that this source is important, 2of14

3 Figure 2. Map of Storglaciären with location of the ZOP surveys, the boreholes involved in the analysis, the thermistor string, and the GPR common offset survey (A B). The shaded area indicates the area where the glacier has a polythermal structure with a cold layer overlying a temperate core. Note that this illustration only gives a schematic representation of the glacier s thermal structure. Further details are given by Pettersson et al. [2003]. especially near the bed in the ablation area, where they calculated water contents greater than 1%. 3. Methods 3.1. Data Collection [11] In July 2008, we collected 100 MHz borehole radar ZOPs using a Måla Geoscience RAMAC GPR system in three boreholes. The holes were approximately 80 m deep and were drilled, with a hot water drill, in the upper ablation area of Storglaciären (Figure 2). From these three boreholes we obtained two ZOPs since one of the boreholes subsequently closed and did not allow further investigation. ZOP is a commonly used geophysical method for obtaining, with high resolution, the radio wave speed structure of the subsurface. This method has been successfully used, for example, to monitor hydrogeological dynamics in the unsaturated zone of aquifers [Binley et al., 2001, 2002] and the spatial distribution of biogenic gas in peatlands [Comas et al., 2005]. [12] In a ZOP survey, an electromagnetic (EM) pulse is radiated from a transmitting antenna (Tx), located in one borehole, and recorded at the receiving antenna (Rx), located in an adjacent borehole (Figure 3). The antennas are then progressively lowered down the two boreholes with the transmitter and receiver at the same depth. We used a 1 m depth step, and for each antenna depth, the time required for EM radiation to travel through the interborehole region was measured along with the received amplitude. At the beginning and the end of every survey, a few traces were collected in the air at a known antenna separation to provide a time zero calibration. Surveyor tripods were used to hold the antennas still during measurements. [13] All the boreholes were terminated englacially to reduce the likelihood of subglacial drainage. The holes remained filled with water for the duration of the study, suggesting that no efficient hydraulic connection was established between the boreholes and the englacial water system. The location of the top of the boreholes was surveyed using differential GPS observations, while the geometry of the holes (i.e., how they deviate from vertical) was measured using an inclinometer (MI 3 Digital Borehole Survey Tools from Icefield Instruments Inc). This instrument determines the geometry of a borehole relative to its top at a series of measurement stations down its length. The orientation is represented by the measured dip and azimuth readings. Measurement stations were collected every 2 m downhole. [14] The borehole area was further investigated during April 2009 when we acquired a 800 m long 25 MHz CO GPR line (A B in Figure 2) to estimate ice thickness and the general hydrothermal structure of the drilling area. A stopand go survey method was used, in which the surface GPR system was held motionless at 0.5 m sampling intervals Radio Wave Speed Profiles With Measurement Error [15] The radar system used in this study required a time zero calibration to correct for the time delay in the equipment electronics. This calibration was done by acquiring a few traces holding both antennas in the air at known antenna separation X. The radio speed in air is v a = m ns 1, and the time delay in the system T DEL is given by T DEL ¼ T a X v a ; where T a is the first break of the wave propagating in the air. After this calibration, the ZOP survey can start, and at any depth, we can calculate the the true travel time across the medium, T M = T P T DEL, where T P is the first break of the in hole recorded wave. The time calibration was repeated at the end of the survey to detect any drift in T DEL which could cause misinterpretation. [16] Distances between the tops of the two boreholes were computed using the easting and northing coordinates from the GPS surveys. Variations in borehole separation with depth were adjusted using the inclinometry data. Travel times and distance were then corrected by considering the Figure 3. Sketch illustrating the geometry of the survey; d w and d i are the propagation paths in water and ice, respectively. ð2þ 3of14

4 Table 1. Standard Errors Associated With the Parameters Used for the Computation of Radio Wave Speed Quantity Error Source (and Units) Error d En d Nn Borehole eastings and northings (m) ±0.05 d X Measuring distance during time zero ±0.02 calibration (m) d Ta Picking first arrival in air (ns) ±0.2 d TP Picking first arrival in ice (ns) ±0.2 d 2dw Error in estimating raypath in boreholes (m) ±0.02 raypath between Tx and Rx antennas to be 2d w + d i (Figure 3), where 2d w = 0.1 ± 0.02 m is the portion of the raypath traveled within the water filled boreholes (consistent with measurements in the field, with error taken into account since the antennas can deviate from the center of the hole), and d i is the distance between the two boreholes in ice. The travel time in ice T i is therefore given by T i ¼ T M 2d w v w ; whereas since at any depth the antenna positions are geometrically described by their easting (E) and northing (N), the actual distance in ice d i is given by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d i ¼ ðe 1 E 2 Þ 2 þðn 1 N 2 Þ 2 2d w ; ð4þ where the subscripts 1 and 2 indicate the transmitting and receiving antennas, respectively. The radio wave speed v i in the glacier ice mixture is then given by d i /T i. The uncertainty in our estimates was calculated using the sources and magnitudes of error listed in Table 1. By applying the formal rules of error propagation [Topping, 1972], we estimated errors in T i and d i of ±0.7 ns and ±0.08 m, respectively. The error in v i varies with T i and d i. Shorter travel times imply less precision in estimating v i. As an example, the error in v i is ±0.001 and ± m ns 1 for distances of 25 and 40 m, respectively Amplitude Profiles With Depth [17] Radar wave amplitude variations with depth throughout the ice column were investigated by studying the first arrivals of the EM pulse propagating within the interborehole region. However, radar data are usually affected by a high amplitude low frequency drift in the recorded signal called wow. The wow observed in the Storglaciären ZOP appears to be a constant whole trace shift, which sets the zero amplitude, presignal noise to negative or positive values. This noise was removed by applying a dewow filter, which subtracted the mean value of a centered time window (length 50 ns) from each sample before amplitude analysis was done. Since further data processing can corrupt the true amplitude response of EM pulses [Yilmaz, 2001], we analyzed dewowed only radar data. Amplitude peaks of the first half cycle of the dewowed wavelet (e.g., from the first break to the following subsequent zero crossing) were measured at each antenna depth and then corrected for geometric spreading. This factor is one of the main energy losses of a wavefront when it travels through a medium [Cerveny and Ravinda, 1971; Sheriff and Geldart, 1995]. ð3þ 3.4. Correcting Speed Estimates for Air Content [18] To estimate the air content distribution within the ice column, we used the model of Bradford et al. [2009], who calculated the air content within the temperate Bench Glacier by considering that according to the ideal gas behavior, the volume of air trapped in the ice varies as a function of temperature and pressure. We can assume that the temperature follows the pressure field [Paterson, 1994]: T ¼ T 0 0 P; where T is the ice temperature, T 0 = K is the triplepoint temperature of water, and b = KPa 1 is the rate of change of melting point with pressure, P, for airsaturated ice [Paterson, 1994]. In the case of ideal gas behavior, we can write the volume concentration of air, a,as a function of pressure: a ¼ K T 0 0 ; ð6þ P where K = R/M a1, a1 is the volume concentration of air within the ice at the glacier surface (with values between 0 and 1 for air contents between 0% and 100%), R = 8.31 J mol 1 K is the universal gas constant, and M = m 3 mol 1 is the molar volume of the gas computed at T 0 and atmospheric pressure P 0 = 88,160 Pa. This value is the average summer value measured at the nearby Tarfala Research Station (Tarfala Research Station, meteorological data, 2009). [19] By ignoring deviatoric stresses from the flow field, the hydrostatic pressure, P z, can be written as a sum of discrete volume elements [Bradford et al., 2009]: P z ¼ g Xn k¼1 ð1 aðkþ Þ i Dz; where g is gravity, r i = 917 kg m 3 is the density of ice, and Dz is the discrete depth step (1 m). The volumetric air content at any particular depth is then given by combining equations (6) and (7) and by adding the contribution of the atmospheric pressure, P 0, to the calculation ð5þ ð7þ KT 0 aðkþ1þ ¼ g i Dz Pn þ K 0 : ð8þ 1 aðkþ P 0 k¼1 The effect of a on radio wave speed estimates can be quantified by considering v m as the bulk radio wave speed in the air ice mixture defined by the sum of volumetric concentrations: v m ¼ð1 a Þv i 0 þ a v a ; ð9þ from which the radio wave speed estimate with the air component removed, v i, is given by v i 0 ¼ v m a v a ð1 a Þ : ð10þ [20] The correction outlined in this section simulates in a reasonable way the decrease of air content with increasing 4of14

5 pressure in glaciers since equation (8) is primarily influenced by the hydrostatic pressure, P z. Numerical tests on equation (8) revealed that deviations from the melting point in the cold layer of Storglaciären (a few kelvin [Pettersson et al., 2003]) have a negligible effect on air content versus depth values. More important errors are introduced by uncertainties in a1. Such errors are included in our estimates using formal error propagation Radio Wave Speed and Water Content [21] In this study we use the Looyenga dielectric mixing formula [Looyenga, 1965] to infer glacier ice properties from derived radio wave speed. A favorable characteristic of Looyenga model is that it makes no assumptions about particle shape. This model has often been used in glaciological water content studies [e.g., Macheret et al., 1993; Moore et al., 1999; Murray et al., 2000b; Benjumea et al., 2003; Navarro et al., 2005; Jania et al., 2005; Barrett et al., 2007; Murray et al., 2007; Gusmeroli et al., 2008]. The Looyenga formulation considers temperate glacier ice as a two phase mixture: ice and inclusion (e.g., air or water), with the volume fraction of the inclusion ( w, between 0 and 1 for inclusion contents between 0% and 100%) given by w ¼ ðc=v i 0 Þ2=3 1=3 i ; ð11þ w 1=3 1=3 i where c = 0.3 m ns 1 is the radio wave speed in air, v i is the measured radio wave speed with the air component removed (equation (10)), and i and w are the relative dielectric constants of ice and inclusion, respectively. This mixture equation is highly sensitive to the relative dielectric contrast between ice ( i = 3.2) and the inclusion ( air =1; water = 80). The small contrast between air and ice causes air content estimates using equation (11) to be especially sensitive to small variations in v i, whereas variations in water inclusions appear to be more robust. The error in w (or a ) estimates is calculated by combining the error in v i with equation (11) using formal error propagation as shown by Barrettetal. [2007]. [22] Water content estimates using the Looyenga equation are typically slightly higher than those derived with other mixture equations such as the Paren [1970] and the complex refractive index models (CRIM) [Greaves et al., 1996]. Exploring the physics behind these models is beyond the scope of this paper. As an example to illustrate the differences, the calculated water content using a radio wave speed of m ns 1 (typical for temperate wet ice) is 0.8%, 0.7%, and 0.6% using the Looyenga, CRIM, and Paren equations, respectively. The differences between these models are similar for commonly observed radio wave speeds in temperate ice and are within the precision of our estimates Measurements of Ice Temperatures and Calorimetric Water Content [23] Radar derived water content measurements were compared to a calorimetric estimate of the same quantity at the CTS by drilling our boreholes near an already established thermistor string (Figure 2). That string was installed to monitor changes of the thermal state of the glacier over time. We obtained vertical temperature distribution by using 18 RTI Electronics, Inc. ACCU CURVE (ACCX 003) thermistors spaced 2 m apart to a depth of 18 m and a 0.5 m separation below 18 m. When the thermistor string was installed, the deepest thermistor had a depth of 29.5 m. The absolute depth for the thermistors changed over time owing to ablation at the surface. Traditional ablation readings of a stake placed next to the thermistor string were performed on a semiweekly basis during the melt season to monitor these depth changes. The resistance of the thermistors was measured every 2 h and was recorded from July 2007 to August The thermistors were calibrated in the same way as reported by Pettersson et al. [2004], and their readings have an uncertainty of ±0.05 C. [24] We also calculated the water content at the freezing front by using the calorimetric method given by Pettersson et al. [2004]. The water content is given by the onedimensional transition condition at the CTS: d CTS dz C p L ¼ wctsa m ; ð12þ where d CTS /dz is the vertical temperature gradient just above the CTS, and C p, L, and are the specific heat capacity, specific latent heat of fusion, and thermal diffusivity of ice, respectively. The volume fraction of liquid water in the temperate ice arriving at the CTS is wcts, and a m is the volume flux of ice through the CTS or the migration rate of the CTS boundary. From the temperature measurements, d CTS /dz can be determined, and it is possible to obtain a m from the temperature measurements over the time when consecutive thermistors in the string freeze into the cold ice. [25] However, the accuracy of the direct observations of the migration rate is often poor because of the large thermistor separation compared to the assumed migration rate. To improve our estimates of the migration rate, we analytically solved the thermodynamic equation for the cold ice [e.g., Pettersson et al., 2004] and found the best fit to the solution by using monthly averages of the measured temperature profile. Evaluating the fitted temperature profile at 0 C gives the position of the CTS and the thermal gradient just above it [Pettersson et al., 2004]. 4. Results 4.1. ZOP and CO Surveys [26] ZOP surveys show that the first arrivals from within the ice column can be clearly identified in the radargrams (Figures 4a, 4b, and 5): the signal to noise ratio is consistently high, even at the largest Tx Rx distances (e.g., 40 m in Figure 4a). The distance between the two boreholes used in the ZOP1 survey changes considerably with depth (Figure 4c), whereas it remains approximately constant in the ZOP2 survey (Figure 4d). This is because one of the boreholes deviated from vertical. First arrivals in the ice are characterized by a clear spike of negative polarity (Figure 5). Anomalously low amplitude first arrivals in some parts of the survey were also observed (arrows in Figures 4 and 5). [27] The resulting radio wave speed profiles together with uncertainties for each survey are shown in Figure 6. Errors in ZOP1 are smaller than in ZOP2. This is because the 5of14

6 is possible to detect the bed reflections in temperate ice [Murray et al., 2000b]. Figure 7b shows the band passfiltered radargram in which a series of weak reflections (indicated with arrows) are distinguishable and interpreted as the bed. The filter employed a cosine ramp between 4 and 8 MHz at the low frequency limit and between 10 and 20 MHz at the high frequency limit. Figure 4. (a, b) Example of 100 MHz ZOP and (c, d) variation of distance between boreholes with depth for the two surveys. ZOP1 (Figures 4a and 4c); ZOP2 (Figures 4b and 4d). Locations in Figure 2. White arrows indicate regions of low amplitude arrivals Water Content Versus Depth Profiles [29] Radio wave speed profiles (Figure 6) are corrected for the presence of air bubbles in order to estimate water content with depth (Figure 8). The radio wave speed measured close to the surface can then be used to estimate air content at the glacier surface, a1 (using equation (11)), the air content distribution with depth (using equation (8)), and consequently, v i at any depth (equation (10)). Calculated values for a1 are 3% ± 1% and 4% ± 2% for ZOP1 and ZOP2, respectively. These values decrease progressively with depth (equation (8)) [Bradford et al., 2009]. Figure 8 shows the resulting water content profiles with depth which were calculated using equation (11). [30] Water content profiles are corroborated by the temperature profile (Figure 8c): the cold surface layer is 20 m interboreholes distance is greater in the former survey. Figure 6 also shows variations in amplitude of the returned signal with depth. Speed values correlate for the two surveys: v m is higher at the surface and decreases gradually with depth until there is a sharp reduction in speed at 21 m depth (CTS). Excluding minor perturbations (e.g., at 20 and 40 m, Figure 6), radio wave speed then tends to stabilize at almost uniform values within the temperate ice, although it appears to decrease somewhat with depth beyond 55 m. Amplitude variations with depth show a few clear minima which are an order of magnitude smaller than the average values throughout the investigated ice column. Two prominent amplitude minima can be identified in the radargrams at 21 and 40 m and clearly correlate with minima in radio wave speeds (Figures 4, 5, and 6). [28] The CO line collected in April 2009 (Figure 7) shows that the ice in our study area is about 130 m thick; the value is calculated using a uniform radio wave speed of m ns 1. The boreholes do not appear in the radargram since they were drilled the summer before. Diffractions that occur through the center of the line are generated by ablation stakes (290, 400, and 500 m in Figure 7a). The first 20 m depth of ice are transparent and correspond to the cold surface layer [Pettersson et al., 2003, 2004]. The scatterer rich ice beneath is interpreted as temperate ice [Pettersson et al., 2003], and this region extends over the entire remaining ice thickness. The cold layer thickness in the drilling area does not vary significantly (Figure 7a, area between dashed lines), meaning that the cold temperate transition surface (CTS) in this region can be approximated as a flat surface. The uppermost boundary of the scattering region is composed of many diffraction hyperbolae. The bed reflection could not be seen in the unfiltered radargram, probably because Storglaciären is temperate for the majority of its thickness. By applying a band pass filter, however, it Figure 5. ZOP2 in wiggle plot format. The first arrivals are clearly identifiable. The arrow indicates an area with anomalously low amplitudes at 21 m, which coincides with the CTS. 6of14

7 Figure 6. Radio wave speed and amplitude profiles (corrected for geometric spreading) with depth at Storglaciären; see Figure 2 for location of the surveys. (a) Speed profiles and (b) amplitude profiles for ZOP1; (c) speed profiles and (d) amplitude profiles for ZOP2. Shaded areas indicate the measurement error. Solid arrows indicate minima in speed, which typically correspond to minima in amplitudes of the received signal; the dashed arrow indicates the minima in speed compared with the synthetic ZOP illustrated in section 5.1. Figure 7. Twenty five megahertz common offset survey line A to B (location in Figure 2) used to determine ice thickness and general thermal structure of the study area. (a) Dewowed only radargram focused on the shallower part of the glacier to show the scattering region and (b) low pass filtered radargram to show the ice thickness. The borehole area was located between the dashed lines. Arrows show inferred bed reflection. 7of14

8 Figure 8. Water content versus depth model obtained from radio wave speed analysis for two ZOP surveys in the ablation area of Storglaciären. (a) ZOP1, (b) ZOP2, and (c) temperature profile from the thermistors string located nearby the ZOP profiles. The cold ice is 21 m thick. Below this depth, the ice is at the pressure melting point and contains water inclusions. Gray dashed line indicates CTS position. The shaded areas represent water content at the CTS measured with calorimetry (note that the measurement was at the CTS only; it is shown throughout the whole ice column to emphasize the uniformity of water content values). thick, and in this layer, the water content in the mws is equal to zero since all the intracrystalline water freezes once below the pressure melting point [e.g., West et al., 2007]. The fact that the cold layer contains no microscopic water is also confirmed by looking at the radio wave speed profiles (Figure 6): speed is always higher than the commonly used value for solid, water free ice (0.168 m ns 1 ). Macroscopic water features can be present in the cold ice (e.g., from percolation of supraglacial water through fractures), but we found no convincing evidence for these since no clear reductions in speed are present in the profiles in Figure 6. Anomalously high water content values (generated from minima in radio wave speed) are observed at the CTS (21 m, supported by the temperature profile in Figure 8c) in both surveys and at 40 m in survey 2 (Figure 8b). At these locations, water content is around twice the mean values measured throughout the rest of the ice column. [31] Satisfactory agreement in terms of both absolute values and general water distribution is observed between the two surveys. The mean water contents in the temperate ice are 0.5% ± 0.3% and 0.7% ± 0.2% for ZOP1 and ZOP2, respectively (stated uncertainties are the mean errors throughout the whole profile). The variability of water content with depth is almost negligible in the temperate ice. Water content values seem to stabilize at values 0.6%. At depths greater than 60 m, the observed decrease in radio wave speed results from slight increases in water content with depth, with values up to 1% in the deepest part of the surveys Temperature Profiles and Calorimetric Water Content [32] Figure 8c shows an average vertical temperature profile for July Because of ablation, the two topmost thermistors melted out or were affected by heat from the surface, so they are not displayed. [33] The position of the CTS in July 2008 (when our ZOP surveys were undertaken) was 6.4 ± 0.2 m from the bottom of the thermistor string according to our analysis. After adjusting for ablation, the CTS depth below the ice surface was 21.3 m. The migration rate of the CTS between May and August 2008 was 1.13 ± 0.18 and 1.23 ± 0.25 m yr 1 over the whole measurement period. The temperature gradient in the cold ice just above the CTS was ± 0.01 Cm 1 in July 2008 and 0.04 ± 0.02 C m 1 for the whole period. These values give a water content of 0.6% ± 0.1% for July 2008 and 0.8% ± 0.1% for the whole measurement period. 5. Discussion 5.1. Hydrothermal Structure of the Study Area [34] Our water content profiles (Figure 8) show that the hydraulic structure of the investigated region of Storglaciären can be summarized as a cold upper layer with 0% of volumetric water content and a temperate core with a water content of 0.6% ± 0.3% (this value results from averaging the two surveys); the water content in the temperate ice does not vary significantly with depth. Calorimetric estimates of water content at the CTS (0.6% ± 0.1%) give results similar to the radar derived values in the upper part of the temperate ice (Figure 8). Discrepancies between calorimetry and radar were observed at the CTS, where the radarderived water content is noticeably higher. These differences can be explained by considering that radar derived water content estimates can be affected by discrete water features; in addition, radar derived water contents are a snapshot in 8of14

9 due to changes of the hydrostatic pressure, (3) water trapped in the ice of the accumulation area at the firn ice transition, and (4) melting due to the strain heating. Sources 1 and 2 are insignificant since the micropermeability of glacier ice is zero [Lliboutry, 1971; Raymond and Harrison, 1975], and source 2 produces negligibly small quantities of water [Pettersson et al., 2004; Aschwanden and Blatter, 2005]. Source 3, as argued by Paterson [1971], is the most important source of liquid water in temperate ice, while source 4 is negligible at the CTS and in the upper part of the temperate ice but becomes significant at depth [Aschwanden and Blatter, 2005]. The observed increase in water content with depth at depths greater than 60 m (Figure 8) can be explained with the predictions of Aschwanden and Blatter [2005, 2009]. Water content increase with depth is also supported by surface radar based measurements in Spitsbergen [Jania et al., 2005] and by calorimetry estimates in the Alps [Vallon et al., 1976]. Figure 9. Simulated ZOP used to understand the potential for misleading interpretations introduced by critical refraction. Antenna separation is 25 m. (a) Schematic of the model input parameters. WC is water content; solid and open dots indicate antenna positions where the first arrivals are direct and critically refracted rays, respectively. Corresponding direct and critically refracted raypaths are indicated with solid and dotted lines, respectively. The low speed (high water content) layer is indicated by the shaded area. (b) Speed models using the parameters illustrated in Figure 9a from direct waves (solid line, solid dots), critically refracted waves (dashed line, open dots), and a comparison between eight antenna depths (from 28 to 35 m) in ZOP1 (dotted line, open squares; dashed arrow in Figure 6). (c) Calculation of h min. time, while calorimetry derived water content is an estimate over a longer interval. [35] Our mean water content values (both from radar and from calorimetry) are within the range of those derived by Pettersson et al. [2004] at the CTS of Storglaciären ( w = 0.6 ± 0.3 in our study in 60 m of temperate ice and 0.8 ± 0.3 at the CTS as given by Pettersson et al. [2004]). By extending the analysis to deeper ice, we have demonstrated that in the upper part of the temperate layer, variations in water content are negligible. Our estimates can be used to calculate ice viscosity for both cold and temperate ice as shown in equation (1). By empirically fitting the experimental results of Duval [1977] to a linear relationship between w and A 0, we calculated A cold = Pa 3 s 1 and A warm = ± Pa 3 s 1 (errors estimated using errors in w ): the whole temperate layer is thus between 3 and 4 times softer than the cold layer, a remarkable difference in terms of ice mechanics. [36] Liquid water in the mws of glaciers potentially originates from four sources [Paterson, 1971]: (1) water input from the surface, (2) changes in the pressure melting point 5.2. ZOP and Water Content: Can We Exclude a Stratified Model? [37] The overall smooth trend of the water content profiles that we observed (Figure 8) shows the uniformity of water content in the mws, and thus, a layered model (e.g., alternation of water free ice and wet ice layers) is not plausible. Such a layered structure can result from the fact that the most important source of water content in glaciers (the entrapment at the close off [Paterson, 1971]) is climatically driven, and thus, it varies in time. For example, a period with high spring melt will produce large volumes of water within the firn aquifer. A low melt period followed by a high melt period could result in the formation of a low water content layer overlain by a high water content layer. [38] The occurrence of critical refractions in ZOP surveys can reduce their ability to detect thin, high water content layers [West and Truss, 2006]. In layered systems, with sharp changes in water content, the first arrival (used to obtain profiles in Figures 6 and 8) may not be the direct raypath propagating between the interborehole region but rather the critically refracted raypath [Rucker and Ferré, 2004]. When a slow speed layer is located between two fast speed layers, the critically refracted path (dotted line in Figure 9a) only partially propagates in the slow layer since it refracts at the interfaces and travels at the faster speed. Critically refracted arrivals cause overestimation of radio wave speed in slow layers [Rucker and Ferré, 2004; West and Truss, 2006]. [39] Nonetheless, the ZOP technique is still used successfully to monitor hydrogeological processes [e.g., Kuroda et al., 2009], and it is possible to validate water content models inferred from the ZOP by identifying potential areas in the ZOP where the first arriving energy does not correspond to the direct raypath [Rucker and Ferré, 2004; Kuroda et al., 2009]. Specifically, where antennas are lowered through a high water content layer that is adjacent to a lower water content layer, the travel time of the critically refracted first arrival will decrease linearly as the antennas approach the boundary with the drier layer [Rucker and Ferré, 2004]. Consequently, a linear decrease in travel time would cause v m to increase linearly if the effects of critical refraction were ignored. Areas where critically refracted energy could be the energy arriving first are marked with arrows in Figure 6. If 9of14

10 such minima in radio wave speed were generated by critically refracted arrivals, it is likely that the water content at these locations would be underestimated. [40] To understand whether these minima in radio wave speed represent high water content layers, we generated a ZOP model [e.g., Rucker and Ferré, 2004; West and Truss, 2006], which simulates a high water content layer surrounded by low water content layers (Figure 9a). The model was run for eight antenna depths to reproduce the minima in speed indicated in Figure 6a, where the speed profile has characteristic features of critically refracted arrivals [Rucker and Ferré, 2004]. The contrast between the wet layer and the two dry layers (Figure 9a) is deliberately set to be high (nowhere in our ZOP do we observe such low radio wave speeds due to high water content) in order to detect any serious misinterpretation of water content in our ZOP. Travel times and corresponding speeds assuming constant antenna separation (25 m) are then calculated using Snell s law, which assumes geometric optics as an approximation of the propagation of EM radiation [Telford et al., 1990] and the equations developed by Rucker and Ferré [2004] for ZOP. Since a pulse generated in the middle of the wet layer will refract critically at the boundary along the upper and lower boundaries with the dry layers, the travel time of the critically refracted raypath is given by [Rucker and Ferré, 2004] t refr ¼ x v high þ z 2 v low cos i c 2 tan i c v high ; ð13þ where v high and v low are radio wave speeds through the dry and the wet layers, respectively, z is the vertical distance from the antenna measurement depth to the interface between the two layers, and i c is the critical angle defined by the Snell s law: i c ¼ sin 1 v low : ð14þ v high [41] Critically refracted waves (Figure 9b) always arrive before the direct arrivals in our model. However, the difference between the radio wave speed measured using the two different arrivals becomes negligible especially in the center of the layer. Figure 9b also shows part of the ZOP1 speed profile (antenna depths between 28 and 35 m; Figure 6, dashed arrow). The speed minima in our data (open squares in Figure 9b) are considerably smaller than the ones caused by the modeled high water content ( w = 1.5%) layer. Even if speed minima in our data set were caused by critically refracted arrivals, the underestimation of water content would only be minor and within the accuracy of our water content estimates (±0.2%). [42] Further evidence of the fact that critical refraction does not corrupt our interpretations is provided by looking at h min, defined as the minimum thickness of a low speed layer for which the direct wave will be first arriving energy [Rucker and Ferré, 2004]: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi v high v low h min x : ð15þ v high þ v low [43] We computed h min from equation (15) using v high = m ns 1 and v low using the likely spectrum of radio wave speeds in temperate ice (from 0.15 to m ns 1 ). Figure 9c shows that the presence of very wet layers (v i = 0.15 m ns 1, water content 2.5%) would be correctly detected without any underestimation of water content if such layers were thicker than 3 m. For greater speeds (i.e., drier layers), the minimum detectable thickness decreases. [44] Since the aim of this modeling exercise was to validate the uniformity of water content in mws, we observe that the occurrence of critically refracted arrivals causes slight underestimation of water content in high water content layers, which are not plausible in our data set since radio wave speed rarely decreases below m ns 1. The presence of high water content layers ( w > 1.5%) is plausible for radio wave speed <0.163 m ns 1, but this case is never observed in our data set Conditions at the CTS and Discrete Macroscopic Water Features [45] It is striking to observe how ZOP derived microcrystalline water content values at the CTS are approximately twice the average values measured in the rest of the temperate ice (Figure 8). This observation indicates that either the water content at the CTS is higher than that of deeper ice or simply that at this position, high water content estimates result from the drop in v m (Figure 6) due to the presence of larger (e.g., centimeter to decimeter size) water features of the MWS crossed by the raypath. Calorimetric water content at the CTS (0.6% ± 0.1%) in fact agrees with the average ZOP derived water content in the uppermost part of the temperate ice (0.6% ± 0.2%). [46] Amplitudes of the first arrivals recorded at the CTS are also considerably lower (1 order of magnitude) than the average amplitudes recorded throughout the whole ice column (Figures 4, 5, and 6). Figure 6 shows how these lowspeed low amplitude arrivals only occur in two regions of the ice column, at the CTS and at 40 m depth. We have no reasons to believe that such an anomalous response would be caused simply by water content changes since this would have been observed more often within the temperate ice. Such a prominent loss of energy can only be explained by scattering and energy partitioning losses when the raypath crosses an interface. It is therefore likely that these minima in v m and amplitude are due to local water features (e.g., water filled fractures [Fountain et al., 2005]) within the interborehole regions. Amplitude profiles, corrected for geometric spreading, presented in this study (Figures 6b and 6d) are only used as a qualitative demonstration of anomalous geophysical response in some regions of the radargrams. More rigorous analysis, incorporating englacial radar attenuation [MacGregor et al., 2007; Matsuoka et al., 2010], should be applied to further explore how radar attenuation changes in response to variations in temperature and water content. [47] We used a travel time model of a ZOP to further explore this possibility and predict the measured radio wave speed when the raypaths intersect water features, such as water filled fractures of variable size. We included only two media, water free ice with uniform radio wave speed v i = m ns 1 and water with radio wave speed v w = m ns 1. We assumed that the distance between the two boreholes, d T, is uniform throughout the profile (10 antenna 10 of 14

11 Figure 10. ZOP model including the presence of large (decimeter size) water features using equation (16), d T =25m,v i = m ns 1, and changing feature size. (a) Schematic of the model setup. Antenna positions in the two boreholes are indicated by the solid dots. The 2 D water feature geometrically described by its width, d w, and height, n. (b, c) Shown is v m for a water feature located at 5 m and between 4 and 6 m depth, respectively. (d) Measured v m for ZOP2 in the depth range m. (e, f) Radio wave amplitude for a water feature located at 5 m and between 4 and 6 m depth, respectively. (g) Normalized amplitude corrected for the geometric spreading measured in ZOP2 in the depth range m (the same range reported in Figure 10d). depths with a 1 m of sampling interval). The water feature in the model is geometrically described by its horizontal width, d w (or the portion of the raypath traveled in water), and height, n, as described in Figure 10a. The true raypath in ice, d i, is thus the difference between d T and d w. [48] With this configuration, the measured radio wave speed, v m, at each antenna depth is given by v m ¼ d T d i =v i þ d w =v w : ð16þ Rearranging equation (16) allows calculation of the fracture width, d w : d w ¼ d T v i v w v w : ð17þ v i v w v m Figures 10b and 10c show the simulation using equation (17) for a 25 m long interborehole region. We observe that even relatively small (e.g., 0.1 m wide) water features can decrease v m and, consequently, cause underestimation of v i. This effect, represented as negative spikes in v m, can be seen in multiple antenna depths depending on the height of the fracture. Minima in speed and amplitude observed in our data at the CTS typically intersect two antenna positions, meaning that the vertical height of the features causing this response is greater than 2 m: for this reason, it is likely that the raypath does not travel around those objects but rather travels through them. [49] We conducted an equivalent study, using the same fracture geometries, for wavelet amplitude. We used the GprMax modeling software [Giannopoulos, 2005] to simulate the radar pulse generated by antenna with infinitesimal 11 of 14

12 size. We assumed the water within the fracture had an electrical conductivity of 0.5 ms m 1, representative of water in glaciers [e.g., Gordon et al., 2001]. We represented the GPR source by a 100 MHz Ricker wavelet [Sheriff and Geldart, 1995]. The maximum amplitude of each arrival was measured from the analytic envelope of each trace, as plotted in Figures 10e and 10f (1 and 2 m high inclusions, respectively). The water feature is clearly associated with a low amplitude anomaly, although differences in amplitude are less marked than the speed anomalies observed previously. Scattering and reflectivity losses are identified as the principal mechanism by which the amplitude anomaly occurs, causing, in the most extreme case (30 cm inclusion in Figure 10), a reduction of 50% with respect to amplitudes observed at 10 m depth; the increases in amplitude that flank this anomaly are tuning (interference) effects between direct wave arrivals and energy scattered from the terminations of the fracture. A skin depth estimate for propagation in water gives the value of 2.3 m: conduction loss in the water is negligible for the size of the feature considered. Despite the simplicity of this model, the size of this anomaly has the same order of magnitude as that observed in Figures 6b and 6d (Figure 10g), and there is even some indication of slight increases at either side of the amplitude minima (Figure 6d). For the narrowest fracture, there is proportionally less reduction in amplitude, attributable to different interference patterns between the direct arrival and multiples within the fracture. This suggests that for a water filled fracture with lowelectrical conductivity, amplitude observations alone cannot be used to characterize fracture geometry in the same way that speed observations can; they are, however, indicative of discrete water features between the boreholes. [50] Fountain et al. [2005] observed that fractures are the main transport route for water from the surface to the englacial system in glaciers and that they are more common than tubular conduits in the overdeepening of Storglaciären. This is the same area of the glacier where our study was conducted. It is therefore likely that such water filled fractures are present at 20 and 40 m depth within the interborehole region in our survey. Such features would cause scattering, loss of energy due to reflection, and increase the travel time of the propagating wave, resulting in coincident low spikes in both measured radio wave amplitude and speed. We can estimate the horizontal width of these fractures (equation (17)) using the average unperturbed speed in the temperate ice (e.g., m ns 1 ) and the measured speed at the negative spike on each case (never lower than m ns 1 ). This calculation suggests that speed minima are caused by water features with d w between 10 and 50 cm, consistent with the fracture interpretation. 6. Conclusion [51] A combination of borehole radar surveys and ice temperature measurements were used to investigate the vertical hydrothermal structure within the ice of the polythermal glacier Storglaciären. The glacier in our study area has a 20 m thick cold, water free layer underlain by a temperate, wet layer. Borehole radar allowed continuous sampling of the dielectric properties of the glacier to a depth of 80 m. The water content distribution appears to be homogeneous throughout temperate layer, except for a slight increase below 60 m, which is consistent with the predictions of Aschwanden and Blatter [2005, 2009]. No evidence in support of a layered structure within the temperate ice was found. We thus propose a simple two layer model comprising an upper water free cold layer and a lower temperate layer with water content of 0.6% ± 0.3%. According to the prevailing views of ice rheology [Duval, 1977; Lliboutry and Duval, 1985], such water content percentages will significantly soften the ice in the study area at Storglaciären. Our calculation based on the measured water content suggests that temperate ice is between 3 and 4 times softer than the cold ice (A cold = Pa 3 s 1, A warm = ± Pa 3 s 1 ). Borehole radar zero offset profiling (ZOP) allows detailed sampling of a glacier s hydraulic structure since variations of radio wave speed with depth can be related to variations in water content. Additionally, anomalously low amplitude low speed regions in the survey can indicate the presence of discrete, decimeter size water features which, in this study, are interpreted as water filled fractures. [52] Our findings suggest that future water content and ice flow models of Storglaciären should consider water contents of 0.6% ± 0.3% throughout the whole temperate ice layer. This value may increase with depth according to theoretical predictions [Aschwanden and Blatter, 2005, 2009]. Deeper borehole geophysical investigations, to the bed of the glacier, are required to elucidate near bed glacier hydrology and thus advance our understanding of polythermal glacier dynamics. [53] Acknowledgments. A.G. is funded by a Swansea University Scholarship, and A.D.B is funded by the GLIMPSE project (Leverhulme Trust Research Leadership Award to T.M.). Fieldwork was funded by the Jeremy Willson Charitable Trust, Consorzio dei Comuni del Bacino Imbrifero Montano dell Adda, Percy Sladen Fund, Mount Everest Foundation, British Society for Geomorphology, Quaternary Research Association, Dudley Stamp Memorial Fund, and Earth and Space Foundation. Partial financial support for P.J. was given by the Swedish Research Council grant B. B. Reinardy, D. Hjelm, R. Scotti, M. Fransci, and T. Enzinger helped in the field. Logistics from the Tarfala Research Station were fundamental for this study. The School of Geography at the University of Leeds let us use its radar system. Discussions with B. Kulessa, R. Clark, B. Barrett, and S. Cook are gratefully acknowledged. We thank A. Smith, T. James, and G. Owen for supporting our efforts to fund the two field seasons reported here. Comments by H. Blatter, our Editor M. Church, F. J. Navarro, J. A. MacGregor, the Associate Editor, and one anonymous reviewer greatly improved the manuscript. References Aschwanden, A., and H. Blatter (2005), Meltwater production due to strain heating in Storglaciären, Sweden, J. Geophys. Res., 110, F04024, doi: /2005jf Aschwanden, A., and H. Blatter (2009), Mathematical modeling and numerical simulation of polythermal glaciers, J. Geophys. Res., 114, F01027, doi: /2008jf Barrett, B. E., T. Murray, and R. Clark (2007), Errors in radar CMP velocity estimates due to survey geometry, and their implication for ice watercontent estimation, J. Environ. Eng. Geophys., 12(1), Benjumea, B., Y. Y. Macheret, F. J. Navarro, and T. Teixidó (2003), Estimation of water content in a temperate glacier from radar and seismic sounding data, Ann. Glaciol., 37, Binley, A., P. Winship, R. Middleton, M. Pokar, and J. West (2001), Highresolution characterization of vadose zone using cross borehole radar, Water Resour. Res., 37(11), Binley, A., P. Winship, L. J. West, M. Pokar, and R. Middleton (2002), Seasonal variation of moisture content in unsaturated sandstone inferred from borehole radar and resistivity profiles, J. Hydrol., 267, of 14