Catchment and grounding line

Figure 1a shows the location of Daugaard Jensen Gletscher overlain with a Landsat image. The catchment boundary was delineated by tracing flowlines upstream from the glacier terminus following the method of Reference Costa-Cabral and BurgesCosta-Cabral and Burges (1994). Flow directions were derived from smoothed fields of gravitational driving stress (GDS) (Reference Le Brocq, Payne and SiegertLe Brocq and others, 2006). The GDSs were based on a digital elevation model (DEM) and an ice-thickness grid of 5 km resolution (Reference Bamber, Layberry and GogineniBamber and others, 2001). The GDS fields were computed at 1 km resolution and linearly smoothed over a distance equivalent to 20 times the ice thickness. The selection of start points at the glacier terminus was restricted to locations covered by the DEM and guided by visual inspection of the ice margins and velocity distribution.

Fig. 1.

(a) Location of Daugaard Jensen Gletscher. The image overlain is a Landsat image. The cyan box shows the region covered in Figure 2 and the red outline shows the catchment boundary. (b) Subsection of an ERS-1 SAR image acquired on 17 March 1993. The image covers approximately 60 km ×60 km and is in slant-range and azimuth coordinates. Heavily crevassed regions, such as the floating tongue and marginal shear regions, enhance the backscatter and are visible as bright regions.

Following Reference Stearns, Hamilton and ReehStearns and others (2005) we assume that the grounding line is located close to where the crevasse pattern on the surface of the glacier changes: as the tongue goes afloat the crevasses become wider. The crevasses are clear in winter synthetic aperture radar (SAR) images (Fig. 1b) where microwaves are able to penetrate dry snow cover and backscatter is high from crevasses, particularly those oriented normal to the incidence angle of the radar.

Intensity feature tracking to measure surface velocities

A time series of surface velocities for Daugaard Jensen Gletscher was generated by applying intensity feature tracking to European Remote-sensing Satellite 1 (ERS-1), ERS-2 and Envisat advanced SAR (ASAR), Landsat-5 Thematic Mapper (TM) band 4 and Landsat-7 Enhanced TM Plus (ETM+) band 8 image pairs. Before tracking, the Landsat-5 and -7 images were resampled using a quadratic interpolation from 30 to 20 m and from 15 to 10 m, respectively, and re-projected to the polar stereographic coordinate system. The SAR images were tracked in slant-range and azimuth geometry after 1×5 multi-looking to a pixel size of ~8m×20 m. This ratio of multi-looking results in approximately square pixels when the displacements are converted to ground range.

The use of feature tracking to measure glacier flow was first demonstrated on optical satellite images (Reference Scambos, Dutkiewicz, Wilson and BindschadlerScambos and others, 1992) and has since been applied successfully to SAR satellite images (Reference Lucchitta, Rosanova and MullinsLucchitta and others, 1995; Reference Luckman, Murray and StrozziLuckman and others, 2002, Reference Luckman, Murray, Jiskoot, Pritchard and Strozzi2003; Reference Strozzi, Luckman, Murray, Wegmuller and WernerStrozzi and others, 2002; Reference Pritchard, Murray, Luckman, Strozzi and BarrPritchard and others, 2005). The method relies on large-scale patterns in image intensity being correlated between successive images. A two-dimensional (2-D) array of offsets is produced between a small patch of intensities from the first image and an equivalent patch in the second image. When the range and azimuth offsets between the two patches match the actual local displacement between the two images, there will be a peak in the intensity cross-correlation. A 2-D second-order polynomial is fitted to the array of correlation values, enabling the position of the peak to be determined with sub-pixel accuracy. By repeating the procedure across the scene, a complete field of local offsets is produced. Here patch sizes of 1000 m×1000m were used over search areas of 3200m×3200m for the SAR images, for which the temporal separation was 35 days, and 800 m×800m over search areas of 1760m×1760m or 2720 m×2720m for the Landsat images, where the temporal separation was either 16 or 32 days, respectively. A spatial sampling for the patches was selected such that offset fields were produced at a resolution of 40 m for all image types.

All offset fields were corrected to a background reference such that non-moving areas were set to zero. The resulting offset fields were filtered according to the signal-to-noise ratio of the correlation peak, and SAR image displacements were converted from slant range and azimuth to surface parallel using orbit data and the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) global DEM (GDEM). The final velocity fields were then filtered by expected downslope flow direction (Reference Luckman, Murray, de Lange and HannaLuckman and others, 2006).

For both SAR and optical data it is necessary to track between pairs of images acquired on the same satellite track in order to preserve the solar and viewing geometries. In total, 135 pairs of Landsat images with temporal separations of either 16 or 32 days were successfully tracked, as well as 53 pairs of SAR images with temporal separations of 35 days.

The errors associated with determination of surface velocity using feature tracking include random errors associated with determination of the 2-D offset and systematic errors associated with re-projection and geolocation. Co-registration of patches with a precision of 1/10 (Reference Gray, Short, Mattar and JezekGray and others, 2001) to 1/20 (Reference Strozzi, Luckman, Murray, Wegmuller and WernerStrozzi and others, 2002) of a pixel is possible, so the errors associated with determining the offsets are, at the most, 0.2 md^–1 for tracking of Landsat-5 images over 16 days, and less for the other image pairs. Errors introduced during subsequent processing are estimated by measuring the mean displacement over a stationary point close to the front of the glacier. For the Landsat-5 images the mean displacement at this point was 0.28 md^–1, for Landsat-7 images it was 0.09md^–1 and for the SAR images it was 0.22 md^–1. Combining the above errors as independent error sources results in a maximum estimated error of 0.34 md^–1.

Frontal positions

Frontal positions were digitized manually on each Landsat and SAR image including those unsuitable for tracking. In addition, a set of Envisat ASAR Wide Swath Mode (WSM) images, covering the ice front between December 2006 and January 2011, were geocoded and used to locate the front position. The intersection points of the digitized fronts with a centre-line profile were used as single-point indicators of midfront position. In total, 214 frontal positions were located on Landsat, 87 on image mode SAR and 658 on WSM SAR images.

Errors in frontal locations can arise as a result of geolocation error and also depend on the precision with which the fronts are digitized. The errors are likely to depend on image type and resolution. Relative errors were estimated by digitizing a section of fjord wall adjacent to the frontal zone. For 30 randomly selected Landsat-5 TM images the standard deviation of the intersection of these vectors with a profile drawn at right angles to the wall was 76 m. The Landsat-7 ETM+ images are of a higher resolution and are more accurately geocoded and are therefore expected to have smaller relative errors. For 30 randomly selected image-mode SAR scenes the corresponding standard deviation was 49 m. The ASAR WSM images are of a coarser resolution than the other images used (100 m), and the frontal positions will therefore have greater random errors. For 90 randomly selected WSM images the standard deviation of the measured position of the fjord wall was 227 m.

Balance fluxes

In order to determine whether Daugaard Jensen Gletscher discharge fluxes are in balance with net accumulation and ablation, modelled SMB values were totalled for each calendar year from 1985 to 2010 over the glacier catchment area.

Runoff, snow accumulation and SMB were modelled for the whole of Greenland using a modified monthly version of the Reference Janssens and HuybrechtsJanssens and Huybrechts (2000) runoff/retention scheme. This model uses monthly average near-surface (2 m) air temperature, based on European Centre for Medium-Range Weather Forecasts (ECMWF) meteorological reanalysis and corrected for Greenland orography errors (Reference Hanna, Huybrechts, Janssens, Cappelen, Steffen and StephensHanna and others, 2005, Reference Hanna2008), to calculate positive degree-days. These parameters are then used together with degree-day factors of 2.7 mm˚C^–1 d^–1 (snow) and 7.2 mm˚C^–1 d^–1 (ice) and an assumed variability of 6 hourly temperatures about the monthly mean – these factors were tuned against previous Greenland field data referenced in Reference Janssens and HuybrechtsJanssens and Huybrechts (2000) – to calculate melt. Monthly precipitation is also used as an input to the model; this too is based on ECMWF reanalysis net precipitation (precipitation minus evaporation and sublimation) data that have been regionally calibrated against the corrected precipitation map of Reference BalesBales and others (2009) to remove spatial biases in the ECMWF precipitation fields. Not all the modelled melt runs off: some is retained in the snowpack as capillary water and partly refreezes as superimposed ice in the surface layer, although obviously some of this superimposed ice subsequently melts. Modelled melt has to reach a certain fraction, typically 0.6, of annual precipitation before surface melt-water runoff is initiated, so the model implicitly includes consideration of the ice–albedo feedback. This Greenland runoff/SMB model set-up has been specially adapted for use with downscaled/gridded meteorological analysis fields and has been used widely in previous studies (e.g. Hanna and others, 2005, 2008, 2009; Reference Sundal, Shepherd, Nienow, Hanna, Palmer and HuybrechtsSundal and others, 2009, Reference Sundal, Shepherd, Nienow, Hanna, Palmer and Huybrechts2011; Reference MurrayMurray and others, 2010). The SMB model output data used in this study have been produced on a 5 km×5 km grid in line with the downscaled meteorological data, based on an accurate DEM for Greenland (Reference EkholmEkholm, 1996; Reference Janssens and HuybrechtsJanssens and Huybrechts, 2000), and can be related to climatic fluctuations at the local-to-regional (drainage basin) scale.

Velocities

Using the Landsat images it is possible to obtain an almost complete spatial coverage of velocity estimates over the lower 30km of the glacier. Figure 2 shows an example of the flow-speed distribution across the glacier obtained by feature tracking between Landsat-5 images acquired on 18 July and 19 August 1986. Not all tracked pairs produced as complete a coverage as this example and the Landsat tracking generally resulted in a better spatial coverage than the SAR tracking. However, the SAR tracking allowed velocities to be derived under cloudy conditions and during the polar night. In this example the speed at the terminus was 11.2±0.3md^–1, falling to 3.0±0.3md^–1 at 45km up-glacier.

Fig. 2.

Results of feature tracking between Landsat-5 images acquired on 18 July and 19 August 1986. The flag marks the location of the extraction point for the time series of velocities presented in Figures 3 and 4.

In total, 188 flow-speed estimates were extracted from the tracking results for a point in the centre of the glacier (marked by the flag in Fig. 2) 5 km upstream of the front close to the point at which the tongue appears to unground, as revealed by increased surface crevassing. The complete time series is shown in Figure 3b. The minimum speed of 7.4±0.3md^–1 occurred in June 1990 and the maximum of 10.0±0.3md^–1 occurred in June 2007. Apart from a few measurements in 2006 and 2007, surface speeds appear to have remained stable throughout the period. There is a consistent seasonal cycle in speed which is easier to identify in Figure 4, in which the last 6 years of measurements are expanded. The timespan covered by these velocity measurements includes periods of cool (1985–95) and then increasing (after 1995) surface air temperatures as reported by coastal weather stations to the north and to the south of Daugaard Jensen Gletscher (Reference Chylek, Dubey and LesinsChylek and others, 2006). There is thus no evidence here that variations in surface air temperatures on the lower reaches of the glacier are having a discernible impact on glacier dynamics over multi-annual timescales.

Fig. 3.

(a) Centre front position relative to most retreated position based on Landsat images and ERS-1 and -2 SAR and Envisat ASAR image mode scenes. (b) Complete time series of velocity magnitudes extracted from a point 5 km upstream of the glacier front (see flag in Fig. 2). In both (a) and (b) Landsat measurements are in blue and SAR measurements are in red.

Fig. 4.

(a) Centre front position relative to most retreated position based on Landsat images (blue) and ERS-1 and -2 SAR and Envisat ASAR image and WSM scenes (red). (b) 2005–10 subset of velocity magnitudes from Figure 3.

Apparent differences between measurements plotted at the same time but from different data sources will be a combination of measurement error and different temporal averaging periods: 16, 32 or 35 days. Twice-daily in situ velocity measurements on the glacier in 1968 and 1972 (Reference Reeh and OlesenReeh and Olesen, 1986) revealed short-period (2–10 day) speed increases of 10–15%, probably related to changes in the subglacial drainage system, and one instance of an acceleration of 50% over a 12–18 hour period coinciding with a lake drainage event 17km upstream of the terminus. These short-period velocity changes can clearly result in discrepancies in velocity estimates based on longer temporal averaging periods when the periods do not exactly overlap.

To reveal the spatial distribution of summer time acceleration of glacier flow, all July Landsat-derived speeds were averaged together and divided by the average of all Landsat-derived speeds. This method is likely to underestimate the maximum acceleration with respect to the annual mean because velocities can only be measured with Landsat images between March and October at this latitude. However, the improved spatial coverage of velocity measurements based on Landsat, compared with SAR, results in a more even distribution of frequency of observations per pixel and, therefore, a spatially smocother representation of the signal.

Figure 5, with the grounding line as identifiable in SAR images (e.g. Fig. 1b) shown in green, shows July accelerations of up to 10% close to the front. This magnitude of seasonal acceleration is typical of stable tidewater glaciers in Greenland (Reference Joughin, Das, King, Smith, Howat and MoonJoughin and others, 2008; Reference AndersenAndersen and others, 2010; Reference Howat, Box, Ahn, Herrington and McFaddenHowat and others, 2010) where the seasonal cycle is governed by meltwater input to the bed. For glaciers where terminus conditions dictate the flow speed, such as Jakobshavn Isbræ on the western coast of Greenland, the magnitude of acceleration can be much higher (Reference Joughin, Das, King, Smith, Howat and MoonJoughin and others, 2008). Upstream of the grounding line, the acceleration factor increases in the along-flow direction where meltwater production is greatest and where it can accumulate from upstream. The acceleration is also greater along a flowline originating from a nunatak. The glacier is heavily crevassed along the region of this flowline, as can be seen in Figure 1b, presumably allowing meltwater greater access to the bed. Reference AndersenAndersen and others (2010) noted that on Helheim Glacier the velocity response to meltwater production was strongest in heavily crevassed regions close to the front.

Fig. 5.

July acceleration factor based on Landsat-only velocity measurements over the period 1985–2010. The grounding line as identifiable in SAR images (e.g. Fig. 1b) is shown in green.

Frontal position and calving

The time series of frontal positions shown in Figures 3a and 4a show that the mean calving-front position remained in a stable position from 1985 to 2010, fluctuating by 1.8km between the most retreated (4 August 2009) and advanced (6 March 2007) positions observed.

Figure 4 includes frontal positions digitized from WSM SAR data and it is easy to identify the occurrence, five or six times a year, of individual cycles of advance and retreat over 0.5–1.0 km. The icebergs seen floating ahead of the calving front in Figure 2 are typical in size and shape for Daugaard Jensen Gletscher and match in width (≥500 m) with the periodic retreats seen in Figure 4. The sawtooth pattern of advance, calving and retreat shown in Figure 4 matches the calving style of a floating ice tongue which emerges as a natural limit of an underlying continuous or discrete fracture process modelled using statistical mechanics (Reference BassisBassis, 2011). It is more difficult to accurately pinpoint the grounding line than the frontal position for the glacier, but there is no evidence of any change in position throughout the 26 year time series.

It is suggested that the –5˚C isotherm for annual mean temperature delimits the minimum latitude of viability for both Antarctic (Reference Vaughan and DoakeVaughan and Doake, 1996) and Greenland (Reference Van der VeenVan der Veen, 2002) ice shelves. The mean annual 2m air temperature (MAT) at the location of Daugaard Jensen Gletscher’s calving front is –5.9˚C and it does maintain a short floating ice tongue, identifiable by the 6 km of heavily crevassed surface extending up-glacier from the front. The MAT considered is the 1958–2010 mean of downscaled (to 5km×5 km resolution) ECMWF meteorological reanalysis data, corrected for orographic errors in the reanalysis and tuned against surface station temperature data. With the exception of –4.6˚C in 1996 all temperatures between 1958 and 2005 were below –5˚C, but in 2006 the MAT rose to –1.9˚C and has since remained above –2.8˚C. If these temperatures persist and the ice-shelf viability limit is indeed –5˚C, it may be that Daugaard Jensen Gletscher will be unable to support a floating tongue in the future.

The behaviour of Daugaard Jensen Gletscher supports the conclusion that for stable glaciers velocity variations due to changes in terminus position are small compared with meltwater-driven velocity variations (Reference Howat, Box, Ahn, Herrington and McFaddenHowat and others, 2010). The onset of summer acceleration is not correlated with any advance/retreat cycle and calving occurs all year round, as can be seen in the WSM frontal position record (Fig. 4). It is more probable that the summer speed-up, which occurs every year, is driven by meltwater penetration to the bed and consequent increases in basal water pressure within an inefficent drainage system allowing enhanced flow.

Mass balance

The modelled 1985–2010 mean annual SMB total for the Daugaard Jensen Gletscher catchment (outlined in Fig. 1) is 9.20 km³w.e., with a standard deviation of 2.0 km³. Reference Stearns, Hamilton and ReehStearns and others (2005) used long-term mean accumulation rates for the catchment based on ice-core data (Reference Bales, McConnell, Mosley-Thompson and CsathoBales and others, 2001; Reference Zwally and GiovinettoZwally and Giovinetto, 2001) to estimate an annual balance flux of 11.4±2.6km³ for a point ~45km further up-glacier. This value agrees, within given errors, with the modelled 1985–2010 mean annual accumulation of 10.65 km³ (standard deviation 2.0 km³). Estimated catchment areas also compare well at 48.5×10³ km² (this study) and 50.0±0.5×10³ km² (Reference Stearns, Hamilton and ReehStearns and others, 2005). Converting the balance flux to a velocity at the grounding line using a mean ice density of 910 kgm^–3, a glacier width of 4.6±0.2 km, a thickness of 555±100m and assuming a rectangular cross section results in a balance velocity of 10.85md^–1. The glacier width was based on a Landsat image. The thickness was based on the typical observed width of capsized icebergs in the fjord plus 60 m. The 60 m allows for a typical basal melt rate close to the grounding line for north Greenland glaciers of 25ma^–1 (Reference Rignot, Gogineni, Joughin and KrabillRignot and others, 2001) and a surface melt rate of 5 ma^–1 (from the modelled rates close to the grounding line) over the ~2 years it takes for ice from the grounding line to reach the calving front.

The error in estimated balance velocity is large: of the order of 35% if the standard deviation of the annual values is used as a measure of the uncertainty in the balance flux. In addition to the estimated errors which may be either positive or negative, the calculated balance velocity is more likely to be an under- than an overestimate of surface velocity at the centre line of a glacier in balance. It is likely to be an underestimate because in converting the balance flux to a surface velocity it was assumed that surface velocities are equal to depth-averaged velocities and that the glacier flows equally fast across the entire width. We also assume that the glacier cross-sectional area is rectangular. It is likely that the depth at the lateral margins is less than that in the centre and that therefore we are overestimating the cross-sectional area.

The measured annual mean surface speed at the grounding line is 8.5 md^–1. This value is a mean of monthly means in order to avoid biasing the value by the greater number of summertime observations. At 10.85 ±3.8md^–1 the computed balance velocity is greater than the measured annual mean surface speed, which would imply that the glacier should be thickening. This result is not consistent with the observations that the region has apparently been losing mass at a rate of 33.5±6.4 Gt a^–1 since 2006 (Reference Schrama and WoutersSchrama and Wouters, 2011) and thinning dynamically by 0.3 ma^–1 during some period between 2002 and 2007 (Reference Pritchard, Arthern, Vaughan and EdwardsPritchard and others, 2009).

The dynamic thinning estimate of 0.3 ma^–1 (Reference Pritchard, Arthern, Vaughan and EdwardsPritchard and others, 2009) was for a point on the glacier at 2000m elevation (71.80˚ N, 30.46˚ W); at this location the mean modelled SMB for the period 1985–2010 is 0.24mw.e. Assuming the thinning is due to ice loss, with a density of 910 kgm^–3, the ratio of actual flux to balance flux would be given by [(0:3 × 0:91) + 0:24]=0:24 = 2:1. So, given a thinning rate of 0.3 ma^–1 we would expect actual fluxes to be at least twice as great as balance fluxes. This inconsistency is most probably due to the high uncertainty in the balance velocity stemming from lack of knowledge of glacier geometric parameters such as ice thickness, rather than an underestimate of the annual mean surface speed.

As well as the dynamic stability, annual totals of modelled SMB for the catchment have also been constant, with a standard deviation of only 2% over the period 1985–2010. Therefore, if Daugaard Jensen Gletscher is flowing at rates greater than the balance velocity, and if it is errors in flux-gate geometry, for example, that make it appear otherwise, it must have been doing so for at least the last 26 years and probably for more than 40 years. This would be consistent with the estimate of Reference Hamilton and WhillansHamilton and Whillans (2002) of thinning over a timescale of 100 years based on mean accumulation rates from ice-core data and GPS-based measurements of vertical velocity.