www.the-cryosphere.net/2/147/2008/ © Author(s) 2008. This work is distributed under the Creative Commons Attribution 3.0 License. The Cryosphere The equilibrium flow and mass balance of the Taku Glacier, Alaska

Abstract. The Taku Glacier, Alaska has advanced 7.5 km since the late nineteenth century, while all other primary outlet glaciers of the Juneau Icefield are in retreat. The Juneau Icefield Research Program has completed field work on the Taku Glacier annually since 1946. The collected observations of surface mass balance, glacier velocity and glacier thickness at Profile IV 29 km above the terminus and 4 km above the equilibrium line provide a means to assess the equilibrium nature of the Taku Glacier. Annual velocity measured and summer velocity measurements completed at a Profile IV from 1950–2006 indicate insignificant variations in velocity seasonally or from year to year. The consistency of velocity over the 56-year period indicates that in the vicinity of the equilibrium line, the flow of the Taku Glacier has been in an equilibrium state. Surface mass balance was positive from 1946–1988 averaging +0.42 m a−1. This led to glacier thickening. From 1988–2006 an important change has occurred and annual balance has been −0.14 m a−1, and the glacier thickness has ceased increasing along Profile IV. Field measurements of ice depth and surface velocity allow calculation of the volume flux at Profile IV. Volume flux is then compared with the surface balance flux from the region of the glacier above Profile IV, determined annually in the field. Above Profile IV the observed mean surface flux from 1950–2006 is 5.50×108 m3 a−1 (±5%), while the calculated volume flux range for the same period flowing through profile IV is 5.00–5.47×108 m3 a−1. The mean surface flux has been greater than the volume flux, which has led to slow thickening of the Taku Glacier up to 1988. The thickening has not led to a change in the flow of Taku Glacier at Profile IV.

Surface mass balance was positive from 1946-1988 averaging +0.42 m a -1 . This led to glacier thickening. From 1988From -2006 an important change has occurred and annual balance has been -0.14m a -1 , and the glacier thickness has ceased increasing along Profile IV.
Field measurements of ice depth and surface velocity allow calculation of the volume flux at Profile IV. Volume flux is then compared with the surface balance flux from the region of the glacier above Profile IV, determined annually in the field. Above Profile IV the observed mean surface flux is 5.50 x 10 8 m 3 /a (+5%), while the calculated volume flux range flowing through profile IV is 5.00-5.47 x 10 8 m 3 /a. The mean surface flux has been greater than the volume flux, which has led to slow thickening of the Taku Glacier up to 1988. The thickening has not led to a change in the flow of Taku Glacier at Profile IV.

INTRODUCTION
Taku Glacier is a temperate, maritime valley glacier in the Coast Mountains of Alaska. With an area of 671 km 2 , it is the principal outlet glacier of the Juneau Icefield (Fig. 1). It attracts special attention because of its continuing, century-long advance (Pelto and Miller, 1990;Post and Motyka, 1995), while every other outlet glaciers of the Juneau Icefield is retreating. Taku Glacier is also noteworthy for its positive mass balance from 1946-1988(Pelto and Miller, 1990, during a period when alpine glacier mass balances have been dominantly negative (Dyugerov and Meier, 1997). Finally, it is unique as the thickest alpine glacier yet measured, with a fjord extending 38-48 km upglacier from its terminus (Nolan et. al., 1995).
The Juneau Icefield Research Program (JIRP) has completed field work on the Taku Glacier annually since 1946 (Miller, 1963;Pelto and Miller, 1990). In this paper we present a data set for the Taku Glacier that is unique in its temporal extent containing: 1) Surface velocity data Profile IV, two parallel transverse profiles, separated by 0.24 km, spanning 56 years (Fig. 2); 2) Seismic profiling depth data along Profile IV; 3) Centerline longitudinal velocity transects from the glacier divide to the ablation zone; and 4) Surface mass balance data from . From this data we determine surface balance and volume balance transfers. This provides a field-based quantitative determination of the volume flux at multiple locations.
Taku Glacier is divided into three zones that describe both mass balance and flow dynamics: (1) The ablation zone, below the mean annual ELA of 925 m (113km 2 ), descends the trunk valley with no tributaries joining the glacier, and only the distributary tongue, Hole in the Wall, leaving the glacier 11 km above the terminus. (2) The lower neve zone, extending from the ELA at 925 m to 1350 m, is a zone where summer ablation is significant (178km 2 ). All the main tributaries (Southwest, West, Matthes, Demorest, and Hades Highway) join in this zone.
Profile IV is in this zone, and comprises the flow of the Matthes and West Branch. (3) The upper neve zone extends from 1350 m to the head of the glacier (380 km 2 ), comprising the principal accumulation region for each tributary except the Southwest Branch. Ablation is limited in this zone, with much of the summer meltwater refreezing within the firnpack. This refreezing results in a unique signature in SAR imagery (Ramage et., al., 2000).
Taku Glacier has been advancing since 1890: It advanced 5.3 km between 1890 and 1948 (Post and Motyka, 1995;Pelto and Miller, 1990). The glacier advanced 1.8 km from 1948-1988(Post and Motyka, 1995, and 0.4 km from 1988 to 2003. The advance rate measured by distance is slowing. The rate of advance is best assessed in terms of area as the terminus lobe is spreading out on a terminus shoal. Post and Motyka (1995) noted that the rate from 1948-slowing of the advance has been attributed to the impedance of the terminus outwash plain shoal (Post and Motyka, 1995), but it has also been conjectured as due to the inability of the mass balance to sustain this advance. With an AAR of 82, Taku Glacier had a continuously positive mass balance from 1946-1994, that has driven the continued advance (Pelto and Miller, 1990). Pelto and Miller (1990) postulated that the positive mass balance from 1946-1985, would drive the continued advance until the end of the century regardless of mass balance in the ensuing years. From 1988-2006 mass balance has been slightly negative, however the glacier has continued to advance as expected.

Surface Mass Balance
JIRP has measured the annual balance of the Taku Glacier from 1946 to 2006 (Pelto and Miller, 1990;Miller and Pelto, 1999). Glacier annual mass balance is the difference between the net snow accumulation and net ablation over one hydrologic year. On non-calving glaciers, such as the present Taku Glacier, surface mass balance observations are used to identify changes in glacier volume. JIRP has relied on applying consistent methods at standard measurement sites (Pelto and Miller, 1990;Miller and Pelto, 1999). On the Taku Glacier 17 test pits at fixed sites are completed directly measuring the snow water equivalent (SWE), the migration of the transient snow line is monitored, and the final ELA position at the end of the balance year is located (Pelto and Miller, 1990). The majority of the snowpits are in the region from 950-1400 m, within 10 km of Profile IV. In 1984, 1998and 2004, JIRP measured the mass balance at an additional 100-500 points with probing transects in the accumulation area to better determine the distribution of accumulation around the test pit locations. Measurements were taken along profiles at 100-250 m intervals. The standard deviation for measurements sites within 3 km, with less than a 100 m elevation change, was +0.09 m/a; this indicates the consistency of mass balance around the test pit sites. Another possible source of error is the assumption that the density measured at test pits is representative of a larger area. However, a study at 40 points within 1 km 2 at different elevations in different years resulted in a standard deviation of ±0.07 m w.e. in a snow pack of 1 to 2 m, displaying the highly uniform density of snow on the Taku Glacier in late summer (Pelto and Miller, 1990).
The measurements of retained accumulation are completed during late July and August and are adjusted to end of the balance year values. This is done via daily ablation rates derived through stake measurements and migration of the transient snow line (Pelto and Miller, 1990;Miller and Pelto, 1999).
Possible errors for the Taku Glacier mass balance record include the sparse density of measurement points (1 per 13 km 2 ), extrapolation to the end of the balance year, infrequent measurements of melting in the ablation zone, and measurements carried out by many different investigators. However, Pelto and Miller (1990), suggest that these sources of error are mitigated by annual measurements at 17 fixed locations, using nine years of ablation data to extrapolate mass balance in the ablation zone, using a balance gradient derived from the 17 fixed sites and known values for the ablation zone that shifts in altitude from year to year based on the ELA, and through supervision of field work by at least one experienced researcher. JIRP has utilized the same methods on the Lemon Creek Glacier where independent long term radar surface profiling has indicated the accuracy of the record (Miller and Pelto, 1999). The principal error is the lack of data from the ablation zone. In this paper we are utilizing data only from the accumulation zone.
An independent measure of mass balance is now available in the form of direct measurement of the surface elevation of the glacier at specific points. The elevation has been determined annually since 1993 at fixed locations along Profile IV using differential GPS as part of the velocity surveying program. GPS annual elevation change measurements along Profile IV at 1100 m show a strong correlation with annual mass balance measurements. This would be expected as elevation at the mean ELA is likely to rise with increased accumulation during years of positive mass balance, and fall with increased ablation during years of negative mass balance.
Glacier dynamics also affect surface elevation, as the glacier can have either an emergent of submergent component to velocity. In the vicinity of the ELA as is the case at Profile IV this factor is minimized. Further the stable velocity indicates that there has not been a change in glacier dynamics that would alter the emergent velocity.

GPS Survey Methods
A key objective of the JIRP surveying program is to collect data that allows quantitative comparison of surface movements and surface elevation change from year to year.
All geodetic observations from 1994-2006 on the icefield are made using a differential GPS method. Profile measurements were determined using the real time kinematic GPS technique, which involved sending a correction signal from the reference station to a mobile rover unit in the glacier divide (located 65 km from the terminus), down to 24 km above the terminus.
The surface velocity was observed at survey locations spaced 0.5 km apart. The surface slope was also determined between each survey location.

Seismic Methods
Seismic methods are required to determine ice depths on transverse profiles because of the thickness of the Taku Glacier (Nolan et. al., 1995). The seismic program completed measurements of ice thickness along eight transects across the glacier, each following the same transects and using the same points used in the GPS movement and elevation surveys.
The seismic methods used for determining ice thickness are typical. A Bison 9024 series seismograph was used with 24 high-frequency (100 Hz) geophones to record the seismic signals produced by explosive charges. The geophones were spaced at 30 meter intervals along profile lines that are perpendicular to the direction of glacier flow, covering 690 meters with each geophone spread. Explosive detonations (shots) were generally made at 500 meter intervals from each end of the geophone spread, to a maximum distance of 2000 meters. Shot and geophone locations were surveyed using standard differential GPS surveying techniques, accurate to +-5 cm. Up to twelve shots were taken on each profile, with up to four reflectors evident on each shot's record. The seismograph was normally set to record two seconds of data, recording at a 0.25 ms sampling rate. The energy for a shot was produced by 4 to 20 sticks of Kinepak (1/3 stick) explosive (ammonium nitrate and petroleum distillate combination), buried approximately 1 meter deep in the firn.
Reflections from the glacier bed were generally clear and easy to recognize on the records by their frequency, character, and distinct moveout times. Migrations were completed using the common-depth-point technique described in Dobrin (1960) and adapted by Sprenke et. al., (1997). Calculations were made using a constant ice velocity of 3660 m/s, a value determined from P-wave first arrival times. The migration and geomorphic profiling process is based on the simplifying assumption that the glacier cross-sections are two-dimensional. The results on Profile IV match closely the results of Nolan et. al., (1995), with a maximum depth of 1450 m in this study versus 1400 m.

Mass Balance
The annual balance record shows a markedly positive trend from 1946-1988 period. The Surface velocity has been constant over a 50-year period on the Taku Glacier at Profile IV ( Figure 5) (Miller, 1963;Dallenbach and Welsch, 1993;Lang, 1997 andMcGee, 2000).
Measurements have focused primarily on summer field measurement of velocity. From 1950From -1993 Profile IV was established in the same location, though there was no means to ascertain that the stakes were positioned identically. In Figure 5  Many temperate glaciers have a substantial component of glacier sliding that depends on bed hydrology, hence displaying seasonal variations. Taku Glacier, however, has exceptionally thick ice, and a low basal gradient. The flow law for internal deformation suggests that negligible basal sliding is taking place in the accumulation zone (Nolan et. al., 1995). The lack of seasonal velocity changes noted in this study and the remarkable uniformity in velocity suggest that sliding is a minor part of the glacier velocity at Profile IV. It is not reasonable to expect a glacier of this size to slow down each fall or winter, and then accelerate to exactly the same speed the following summer. The greatest thickness of the Taku Glacier was noted to be 1477 m at Goat Ridge, 22 km above the terminus (Nolan et. al., 1995). The centerline depth of the glacier is greater than 1400

CALCULATION OF VOLUME FLUX
With direct measurement of surface velocity, ice thickness and width for each increment of glacier width on the profiles, the only unknown in determining volume flux is determination of depth average velocity. Several points led Nolan et. al., (1995) to conclude that basal sliding is minimal, most importantly, calculation of a basal shear stress of 125 kPa. We determined basal shear stress to be 120-180 kPa along Profile IV. These values are beyond that at which substantial basal sliding would be anticipated. In addition, the consistency in velocity each summer and in annual velocity indicates that there is negligible seasonal fluctuation in velocity in the vicinity of profile IV. Seasonal fluctuations are generally the result of changes in sliding.
To determine depth average velocity (U d ) we have applied the equation (1) (van der Veen, 1999;Nick et. al., 2007), using values from the center of the glacier.
where A=4.6 x10 -10 kpa -3 day -1 is the rate factor (Paterson, 1981), n=3 is the flow-law exponent, H is the measured ice thickness (1400 m) and S d the basal shear stress noted above (125-180 kpa)(or basal drag). Plugging these values into equations (1) gives U d = (2)( 4.6 x10 -10 kpa -3 day -1 )(1400)/5 x (120 3 )=0.45 m day -1 The lower value for basal shear stress is used at the suggestion of van der Veen (1999)  The mean U s velocity between each two survey flags is used to represent the average U s for that width increment of the glacier. The mean depth for that width increment from the seismic profile is then determined. The product of the width of the increment and depth of the increment provide the mean cross sectional area. The mean U s for each increment is converted to a mean U d using equation (

CONCLUSION
The results indicate that Taku Glacier has had an equilibrium flow, with no significant annual velocity changes in the last 50 years. Furthermore, although seasonal variations had been expected (Miller, 1963), observations of velocity throughout the year indicate no seasonal variations, probably due to high basal shear stress which prevents sliding. The surface mass balance accumulating above Profile IV in the last half century is in excess of the volume flux through the profile. The result, supported by both survey results of JIRP and radio echo sounding by the University of Alaska-Fairbanks (Nolan et al., 1995), is glacier thickening. The sustained thickening, positive balance, and consistent flux of the 1946-1988 period suggested that the glacier terminus would continue to advance (Pelto and Miller, 1990). From 1988From -2005 the mass balance has been slightly negative, and the glacier has thinned slightly ( Figure 3) though the volume flux at Profile IV has not declined appreciably. The significant change in glacier mass balance beginning in 1988 is expected to influence the glacier velocity, volume flux and eventually the terminus, if it is sustained for another 20+ years. A reduced mass balance, along with the proglacial delta and expanding front of the glacier noted by Post and Motyka (1995), would lead to a reduction in the advance rate. The glacier velocity did not change appreciably as the glacier thickened by 10-20 m at Profile IV and it is expected that it would take a thinning of more than this to substantially alter glacier velocity.