Lake-calving glaciers

The dynamics of tidewater glaciers have received much attention because the large and rapid mass losses often associated with instability of these glaciers is important for sea-level rise (Reference MeierMeier and others, 2007; Reference Pfeffer, Harper and O’NeelPfeffer and others, 2008). However, much less is known about the contributions to sea-level rise from lake-calving (lacustrine) glacier systems despite the growing number of such systems worldwide. Proglacial lakes commonly form at the termini of glaciers as they retreat through overdeepened channels formed by glacier erosion (Reference Warren and AniyaWarren and Aniya, 1999). These proglacial lakes can then modify glacier behavior through flotation, increased calving and ice flow, and accelerating terminus retreat (e.g. Reference Funk and RöthlisbergerFunk and Röthlisberger, 1989; Reference Warren and KirkbrideWarren and Kirkbride, 2003). The shift in terminus dynamics can play a significant role in lacustrine situations at many spatial scales ranging from small alpine glaciers terminating in cirque basins to valley lakes (Reference Boyce, Motyka and TrufferBoyce and others, 2007; Reference Dykes, Brook and WinklerDykes and others, 2010), to large lake-calving glaciers such as those in Patagonia (Reference Warren, Greene and GlasserWarren and others, 1995; Reference Warren and AniyaWarren and Aniya, 1999; Reference Naruse and SkvarcaNaruse and Skvarca, 2000; Reference Warren, Benn, Winchester and HarrisonWarren and others, 2001), to lakes surrounding the Laurentide ice sheet at the end of the Last Glacial Maximum (Reference Cutler, Mickelson, Colgan, MacAyeal and ParizekCutler and others, 2001). The current melting and retreat of the Greenland ice sheet is likely to increase the number of ice-marginal lakes there, introducing another component of dynamic and accelerated ice loss. Data on calving flux, ice flow and surface mass balance on lake-calving glaciers are, with few exceptions, virtually nonexistent. Thus it is difficult to assess the relative importance of overall ice loss for lake-terminating glaciers and its relevance to global sea-level rise.

Most glaciers along the Gulf of Alaska have been retreating and thinning since achieving their Little Ice Age (LIA) maximums sometime between AD 1750 and 1900, in some cases quite rapidly. This ice loss has contributed significantly to rising sea level and has been linked to climate warming (Reference Arendt, Echelmeyer, Harrison, Lingle and ValentineArendt and others, 2002). In fact, a majority of temperate mountain glaciers worldwide are thinning and retreating (Reference SolomonSolomon and others, 2007). Although their volume is a small percentage of the world’s total land ice mass, they are important contributors to global sea-level rise (Reference MeierMeier and others, 2007; Reference Pfeffer, Harper and O’NeelPfeffer and others, 2008; Reference Radić and HockRadić and Hock, 2011). During the period 1962–2006, Alaskan glaciers were responsible for 7.5% of the recent estimate of sea-level rise (Reference Berthier, Schiefer, Clarke, Menounos and RémyBerthier and others, 2010). The relationship between glacier thinning/retreat and climate is complicated for glaciers that lose mass through calving (Reference Post, O’Neel, Motyka and StrevelerPost and others, 2011). Calving is an important ice-loss mechanism, and can result in much larger volume loss than would be possible through surface ablation alone (Reference Van der VeenVan der Veen, 2002). However, studies have shown that calving rates for lake-terminating glaciers tend to be much lower (by up to an order of magnitude) than for their tidewater calving cousins for equivalent water depths (for reviews see Reference Van der VeenVan der Veen, 2002; Reference Benn, Warren and MottramBenn and others, 2007). Furthermore, near-terminus surface slopes of tidewater glaciers are typically steeper than lake-calving termini, resulting in near-terminus ice speeds differing by an order of magnitude, with retreating tidewater glaciers often flowing at speeds of 5–10 km a⁻¹ compared to 100–1000 m a⁻¹ for lake-terminating glaciers.

The reasons for the major differences in terminus dynamics between tidewater and lake-calving glaciers remain unexplained. We can distinguish at least three environmental factors that may be partially responsible for these differences: (1) tidal forcing only affects tidewater glaciers, (2) a strong density contrast exists between fresh water and sea water for tidal systems, and (3) glacial lakes tend to be colder and less stratified as lakes are closed basins with no heat exchange with the ocean. These differences result in very different circulation patterns, which can drive heat transport and influence calving rates. Despite these differences, calving losses can play a significant role in glacier mass balance for lake-terminating glaciers. For example, calving losses at Glaciar Perito Moreno, Patagonia, account for 40% of total ice loss there (Reference Stuefer, Rott and SkvarcaStuefer and others, 2007). At the other extreme, calving losses at Mendenhall Glacier, a small valley glacier near Juneau, Alaska, USA, account for only 4% of the total ice loss (Reference Motyka, Hunter, Echelmeyer and ConnorMotyka and others, 2003a; Reference Boyce, Motyka and TrufferBoyce and others, 2007). As with tidewater glaciers, retreat of lake-terminating glaciers into deeper water can result in positive feedback: as the terminus approaches and exceeds flotation, ice flow may accelerate, causing drawdown of up-glacier ice and extensional thinning. The terminus eventually breaks up into large tabular blocks as ice weakens and fractures. In southeast Alaska, Reference Larsen, Motyka, Arendt, Echelmeyer and GeisslerLarsen and others (2007) found that calving glaciers accounted for over two-thirds of the ice loss and found that lake-calving glaciers thinned faster per unit area than tidewater glaciers. Yakutat Glacier (Fig. 1a) was identified as having one of the highest rates of ice loss during the period 1948–2000 (Reference Larsen, Motyka, Arendt, Echelmeyer and GeisslerLarsen and others, 2007).

Fig. 1.

(a) Yakutat Icefield with Yakutat, Hidden, West Nunatak, East Nunatak, Battle and Novatak Glaciers. The LIA extents at the southern tip of Russell Fjord and for Yakutat Glacier are shown in dashed white. (b) Terminus area of Yakutat Glacier, 17 July 2009.

In this paper, we investigate the continued ice loss of the Yakutat Ice Field (YIF), focusing on the period 2000–10. We use three digital elevation models (DEMs), one from NASA Shuttle Radar Topography Mission (SRTM) and two from Système Pour l’Observation de la Terre (SPOT) imagery. Lidar profiles, flown nearly concurrently with the SPOT image acquisitions, provide a check on SPOT DEM reliability. We partition mass loss due to calving vs surface mass balance in order to determine their relative contributions and to assess the role of glacier dynamics in ice loss. The YIF consists of both land-terminating and lake-calving glaciers, thus allowing comparison of ice losses from systems experiencing different terminus dynamics, but which are affected by the same climate.

Study area

Yakutat Glacier (337 km²; Reference RaupRaup and others, 2007) lies on the western (maritime) side of the northern Brabazon Range in southeast Alaska, 50 km east of the town of Yakutat (Fig. 1a), where annual precipitation rates exceed 3800 mm a⁻¹ (http://paya.arh.noaa.gov/clim.php). The glacier is the main outlet of the 810 km² YIF (Reference RaupRaup and others, 2007) and consists of two main tributaries, each ∼ 25 km long, that flow from ice divides at 700 m elevation. Until 2010, the tributaries joined in Harlequin Lake (elevation 28 m) and terminated in a 5 km wide lake-calving front (Fig. 1b). The 1973–82 equilibrium-line altitude (ELA) at nearby Variegated Glacier averaged ∼1000 m, with annual variations of up to 300 m (Reference Eisen, Harrison and RaymondEisen and others, 2001). Thus, YIF’s highest surface elevation is at or below the current ELA for this region, thereby ensuring continuing glacier thinning.

Yakutat Glacier began retreating after reaching its LIA maximum, which likely occurred during the mid-18th century (Reference Barclay, Calkin and WilesBarclay and others, 2001). By 1903, Harlequin Lake had begun to form as the glacier retreated into an over-deepened basin (Fig. 2; International Boundary Commission (IBC) maps, IBC, 1952). Harlequin Lake continued to expand as the glacier retreated another 13 km during the 20th century. The lake area was 69 km² in 2010. Yakutat Glacier thinned at an average rate of 2.7 ± 0.3 m w.e. a⁻¹ between 1948 and 2000 (Reference Larsen, Motyka, Arendt, Echelmeyer and GeisslerLarsen and others, 2007), with similar rates observed at other YIF glaciers. This rapid ice loss has resulted in solid-Earth uplift rates from glacier rebound which are currently among the highest in the world (∼32 mm a⁻¹; Reference Larsen, Motyka, Freymueller, Echelmeyer and IvinsLarsen and others, 2005). IBC maps indicate that East and West Nunatak Glaciers were still connected at the terminus and calved into Nunatak Fjord (Fig. 2). These glaciers are now land-terminating and have been for at least half a century.

Fig. 2.

IBC map from 1903 (IBC, 1952) showing the YIF with (1) Yakutat Glacier, (2) Novatak Glacier, (3) Battle Glacier, (4) East Nunatak Glacier, (5) West Nunatak Glacier and (6) Hidden Glacier. Glacier outlines in bold black depict the glacier extent in 2005, based on the GLIMS database. Proglacial Harlequin Lake began forming in 1903, when Nunatak Glacier was still a tidewater glacier (1903 outline in fine black).

Digital elevation models

We compared three DEMs from 2000, 2007 and 2010 to evaluate glacier thinning. The first DEM was derived from C-band data of the SRTM collected in February 2000, with a spatial resolution of 1 arcsec or ∼30 m (Reference Rodríguez, Morris and BelzRodríguez and others, 2006). Reference Larsen, Motyka, Arendt, Echelmeyer and GeisslerLarsen and others (2007) compared the SRTM DEM to lidar profiles flown over southeast Alaska to obtain an estimate of SRTM vertical uncertainties. Their analysis resulted in an elevation-dependent correction to address seasonal differences and radar penetration and also provided an estimated gridpoint uncertainty of 5 m. We have adopted these results for our comparisons of the YIF SRTM DEM to other DEMs.

The other two DEMs have a spatial resolution of 40 m and were generated from SPOT 5 imagery, acquired on 3 September 2007 and 20 September 2010 (Reference Korona, Berthier, Bernard, Rémy and ThouvenotKorona and others, 2009). We masked poorly resolved areas using boundaries supplied with the DEMs. In order to evaluate and correct any elevation errors we compared SPOT DEMs over the YIF to light-aircraft laser altimetry acquired under Operation Ice-Bridge (Reference LarsenLarsen, 2010) and earlier University of Alaska Fairbanks glacier altimetry. Lidar data were obtained on 26 August 2007 in profile mode (vertical precision 10.3 m and point-spacing 1.2 m) and on 29 August 2010 in scanning mode (vertical precision ±0.3 m and point-spacing 1 m⁻²), 8 and 22 days before SPOT acquisitions. We corrected for melt between the lidar and SPOT acquisition dates. Measurements of summer mass balance for Yakutat Glacier from 2009 and 2010 showed a linear relationship between elevation and melt. A linear function based on these data was then combined with the mean melt recorded by ablation meters (Reference Bøggild, Olesen, Ahlstrøm and JørgensenBøggild and others, 2004) on the floating tongue (0.08 m d⁻¹) to obtain a melting correction for the dates of the 2007 lidar and SPOT DEM. We estimate the associated uncertainty at ±0.1 m. The same method was used to correct for melting between the 2010 SPOT DEM and lidar data, except only August 2010 ablation-meter (∼− 0.08 m d⁻¹) and summer mass-balance data were used.

Elevation differences between lidar data and the SPOT DEMs were approximately normally distributed, with some outliers at either end. Most of these occur in crevassed terminus regions. The others occur over steep bedrock nunataks near the ice divide and probably reflect the difference in grid resolution between the two datasets. We therefore filtered out clear outliers with elevation differences exceeding ±10 m, and then corrected for melt as outlined above. The elevation differences for both uncorrected and corrected data are shown in Figure 3. The corrected differences were then used to define a linear elevation-dependent vertical bias correction for both years, which was applied to the original SPOT DEMs before differencing.

Fig. 3.

Distribution of laser altimetry minus SPOT elevation differences flown over the YIF. The raw data (gray) were corrected by excluding elevation differences exceeding ±10 m and by applying an elevation-dependent melt correction function (black). The black curve is a normal fit over the corrected distribution, and the dashed gray curve represents a normal fit through raw data. Vertical bars illustrate the area within the standard deviation.

Digital elevation model differencing

We differenced the DEMs using Quick Terrain Modeler (version 7.1.2) to produce an elevation-change (ΔZ) DEM with grid spacing of 40 m. The glacier mask for the YIF was created using data from GLIMS (Global Land Ice Measurements from Space; Reference RaupRaup and others, 2007), Landsat imagery and USGS (US Geological Survey) Topo maps.

Elevation changes at the glacier margins along steep valley walls can be poorly resolved due to grid spacing and mismatched gridpoints. Thus, the mask was downscaled by two pixels (pixel size 40 m × 40 m) along the edges to minimize such errors. Outliers in the ΔZ distribution (Fig. 3) are from snow-covered areas, where the uncertainty of the DEM is large, and from glacier margins. The latter are most likely an artifact of edge proximity that was not caught by downsizing the outline mask. Thus, pixels with ΔZ greater than +35 m (0.04% of the YIF) and less than −105 m (<0.01%) for 2000–07, and greater than +15 m (0.15%) and less than −45 m (0.01%) for 2007–10, were eliminated.

We neglected uplift and assumed no changes in elevation of the glacier bed, such as may be caused by erosion and sediment deposition. The uplift rate in the YIF area, 32 mm a⁻¹ (Reference Larsen, Motyka, Freymueller, Echelmeyer and IvinsLarsen and others, 2005), although large, is negligible compared to the mean ΔH = Δt of the ice field. With the exception of the floating terminus of the YIF, ΔZ derived from the differenced DEM can be used directly to calculate ice volume change and thinning rates, ΔH = Δt. However, a different strategy must be employed when assessing ice loss for the floating terminus of Yakutat Glacier. We identify four zones: (1) grounded ice, (2) free-floating ice, (3) a transition zone between the two, and (4) the area of terminus that retreated between dates of the DEMs (see Appendix). Figure 4c and d show the locations of a series of transects through the differenced DEMs. The change in ΔZ along these transects helps define these different zones (Fig. 4f and g). For grounded ice, ΔZ is a direct measure of ice loss. For the floating tongue, buoyancy must be taken into account. Here we assume hydrostatic equilibrium with an ice density of 900 kg m⁻³ and freshwater density of 1000 kg m⁻³ so that ice thinning is given by ΔH = 10ΔZ. Ice in the transition zone was originally grounded but is now floating. To assess ΔH, we apply a linear trend as a function of distance to evaluate ΔH between the grounding line and the floating tongue.

Fig. 4.

(a, b) Glacier surface elevation change rates (ΔZ/Δt; m a⁻¹) of the YIF before correcting for the floating tongue: (a) 2000–07 and (b) 2007–10. (c, d) Elevation changes ΔZ and locations of transects for (c) 2000–07 and (d) 2007–10. (e) The corrected ice thickness change ΔH (2000–07). (f, g) The transects of the terminus area ((c) and (d) for location) used to define a transition zone between the grounded ice (right side of each panel defined by large ΔZ) and the floating tongue (left side). Black transects were derived from the western part of the terminus, and gray from the eastern part. Points mark the change from one zone to another (squares for the western, triangles for the eastern part). Dashed lines represent the mean ΔZ for the floating (upper) line and grounding (lower) line, based on the hand-picked points.

The fourth zone, the area of the terminus retreat, was identified using SRTM and SPOT images. The area of retreat was assumed to have been in hydrostatic equilibrium, so surface elevations derived from the DEMs were multiplied by 10 to determine total ice loss. Some regions near lateral margins are likely partially grounded, so corrections were made for these regions. All four zones changed over time and were determined separately for 2000–07 and 2007–10. Details of the treatment of the four zones are provided in the Appendix.

Our geodetic DEM differencing approach assesses the total mass loss of the YIF, including surface mass balance and mass loss due to calving. Retreat of a floating tongue does not lead to mass changes in the local glacier–lake system, and in the transition zone only a portion of the thinning ice leaves the lake–glacier system. To allow comparisons to other results, we evaluate ice loss in two different ways. For example, sensors such as GRACE (Gravity Recovery and Climate Experiment) only measure total mass change, which directly translates to eustatic sea-level rise. However, mass-balance studies need to account for all ice that is lost, regardless of whether some of the meltwater remains in the lake. In neither case do the values follow directly from measured ΔZ.

We now address the question of estimating the uncertainty of determining volume change and geodetic mass balance. The total change in ice volume is determined by differencing the DEMs and summing gridpoints either over the area of the YIF or over individual glaciers. The volume change can in turn be converted to mass (expressed as water equivalent volume, w.e.) if the ice density is known, and further converted to an area-wide specific mass balance by dividing by the area.

When estimating the uncertainty of such calculations, two extreme approaches have commonly been applied (Reference Rolstad, Haug and DenbyRolstad and others, 2009). One approach uses the uncertainty of point measurements (i.e. the standard deviation of the elevation error) to represent the integrated uncertainty: the point uncertainty is essentially treated as being totally correlated across the area of integration (Reference Cox and MarchCox and March, 2004; Reference Larsen, Motyka, Arendt, Echelmeyer and GeisslerLarsen and others, 2007). At the other extreme, uncertainties of point measurements are treated as random uncorrelated errors (Reference Rignot, Rivera and CasassaRignot and others, 2003). In this case, uncorrelated integrated errors will be a factor n ^1/2 smaller than correlated errors, where n is the number of gridpoints over which the spatial integration is carried out. Following methodology developed by Reference Rolstad, Haug and DenbyRolstad and others (2009) and outlined in Reference Motyka, Fahnestock and TrufferMotyka and others (2010), we chose an intermediate method of estimating uncertainties, that of using variograms of the differenced DEMs over adjacent land areas to determine an area of correlation, A _c, which is then taken as a measure of error correlation between the two DEMs over the ice.

For comparison of the SPOT DEMs, we found A _c = 0.07 km², which is considerably smaller then the area, A, both for the YIF (810 km²) and for the individual glaciers. Table 1 provides the variance of the mean of the area, σ _ΔA , and σ_V , the uncertainty in volume change, calculated using relationships discussed in Reference Motyka, Fahnestock and TrufferMotyka and others (2010).

Table 1

Area and volume changes for glaciers comprising the YIF: lake-calving Yakutat and Battle Glaciers and the other, land-terminating, glaciers. The three different lines for Yakutat Glacier reflect uncorrected values, values corrected for the floating tongue in terms of ice loss (MB) and values corrected for mass loss of the glacier–lake system (SLR). ΔV is the volume change, σ _ΔA is the area elevation uncertainty, σ_V is the volume change uncertainty (1 for a correlated uncertainty and 2 for an assumed correlation length of 150 m) and is the mean mass balance. The accumulation–area ratio (AAR) was derived from the 2007 SPOT DEM

Assessing similar uncertainties for the SRTM vs 2007 SPOT DEMs is more problematic as we are unable to derive suitable variograms due to the seasonal difference. In the most pessimistic case we assume that the elevation difference uncertainty of 5.5 m is correlated across the entire area. The corresponding uncertainty in volume change for YIF is then 4.5 km³ compared to 0.25 km³ for an assumed correlation length of 150 m (Table 1).

Additional uncertainties accrue from our treatment of the floating tongue. These uncertainties are discussed in the Appendix: they increase the uncertainty in volume change of Yakutat Glacier by 0.01 km³ but do not influence the remainder of the YIF. Uncertainties due to changes in ice and firn density are considered negligible here, since almost all of the YIF glacier area is below the snowline.

Calving flux

Calving flux Q_c (m³ a⁻¹)is the difference between ice flux arriving at the calving front and the volume change at the terminus (advance/retreat):

where Q _in is the ice flux and rate of retreat is (Reference O’Neel, Echelmeyer and MotykaO’Neel and others, 2003).

Long-term retreat

We estimated long-term thinning of the YIF by comparing center-line contour crossing elevations from 1903 IBC maps (cf. Fig. 2) to the 2010 SPOT DEM. Based on comparisons of land features to USGS Topo maps, the uncertainty for the IBC map elevations is ∼40 m (half contour interval). For reconstruction of the terminus retreat during the 20th century, we used terminus outlines derived from IBC maps (1903), an air photo by B. Washburn (1934), a US National Elevation Dataset (NED) DEM (1948), air photos by A. Post (1960–78) and Landsat imagery (1973–2010). The outlines were digitized and georeferenced by hand using the software ENVI (version 4.4). We calculated retreat by determining the area defined by a 1400 m wide bar intersecting with terminus positions to ensure a representative retreat rate.

DEM differencing

DEM differencing revealed that the entire YIF experienced strong thinning for both periods. Thinning rates ranged from 3.0 to 2.0 m a⁻¹ at the ice divides and increased down-glacier to ∼10.5 m a⁻¹ near the terminus of Yakutat Glacier (Fig. 4a and b). The total ice volume loss and mean mass balance between 2000–07 and 2007–10 for the YIF and for the individual glaciers comprising the YIF are summarized in Table 1, together with error estimates. Table 2 presents results specific to Yakutat Glacier. We report results from DEM differencing with and without corrections for the floating terminus. Ice losses in the region of the floating tongue were evaluated as described in the Methods section and Appendix: one for mass-balance calculations and the other for sea-level rise comparison (Table 2). Figure 4e shows the differenced DEM (2000–07) of the terminus area of Yakutat Glacier with its floating tongue and after corrections have been applied.

Table 2.

Volume change for the different zones of Yakutat Glacier resulting from DEM differencing. MB denotes mass-balance calculations, and SLR the contribution to sea-level rise

Lake-calving Yakutat Glacier experienced the highest area-averaged mass balance of the YIF: −4.76 ± 0.06 and −3.66 ± 0.05 m w.e. a⁻¹ for 2000–07 and 2007–10 respectively (Fig. 4a and b; Table 1). In contrast, land-terminating glaciers experienced typically ∼1 m w.e. a⁻¹ less mass loss than Yakutat Glacier.

Calving flux

Long-term retreat

To complement and provide perspective on the recent volume losses we also examined long-term trends in thinning and glacier retreat by comparing the center-line elevation of the 1903 IBC maps to the 2010 SPOT DEM (Fig. 6a), and by plotting terminus positions derived from a variety of resources (Fig. 6b and c).

Fig. 6.

Evolution of terminus retreat between 1903 and 2010. (a) Elevation of the center line of Yakutat Glacier in 1903 (solid) and 2010 (dashed) for west branch (black) and east branch (gray). Elevation difference (1903–2010) of west branch (black) and east branch (gray) in the lower panel. (b) Selected terminus positions overlaying the 2010 SPOT image. (c) Terminus retreat in relation to the terminus position in 1903 (purple) and retreat rates (green). Detailed data in dashed black box are shown in the lower panel.

Although glacier contours on the 1903 IBC maps have large uncertainties (±40 m), they do provide some quantification of total ice loss that has occurred over the last century. For example, the ice surface dropped by ∼400 m during the last century in the region of the 2010 terminus. The maps also suggest that the divides at Yakutat Glacier were about 100 and 200 m higher on the west and east branches respectively than they are today.

The outlines of glaciers comprising the YIF in 1903 (from IBC maps) vs 2005 (GLIMS) illustrate the degree of retreat that has occurred during the last century (Fig. 2). East and West Nunatak were connected as one tidewater glacier in 1903. By 2005 the glacier branches had separated and had retreated 13 and 10.5 km respectively. Both now terminate on land. Hidden Glacier underwent a retreat of ∼7.1 km and Novatak Glacier experienced ∼3.1 km terminus retreat between 1903 and 2005, whereas Battle Glacier does not appear to have retreated during this period. Yakutat Glacier retreated ∼14 km, albeit at highly variable rates.

Recent ice losses and comparison to other studies

Yakutat Ice Field experienced a total volume loss of 31.77 ± 0.31 km³ between 2000 and 2010, for an average of 3.18 ± 0.03 km³ a⁻¹ (Table 1). This includes a correction for the elevation change of the floating tongue, which amounts to 5.9% of the total for the first period (2000–07) and 11.2% for the second period (2007–10). Corrections for mass loss calculations of the glacier–lake system are small. For geodetic mass-balance calculations (m w.e.a⁻¹) we use mass balance, which includes all ice losses (Table 2). Previous studies did not include this correction. We report our results for mass balance both with and without the floating-tongue contribution. Reference Larsen, Motyka, Arendt, Echelmeyer and GeisslerLarsen and others (2007) differenced DEMs from the 1948/62 US National Elevation Dataset (NED) and the 2000 SRTM and obtained an average mass balance of −2.7 m w.e. a⁻¹ over this time-span. Similar results (−2.5 m w.e. a⁻¹) were reported by Reference Berthier, Schiefer, Clarke, Menounos and RémyBerthier and others (2010) for DEMs from the NED and 2007 SPOT. However, they did not apply the seasonal difference correction as done here from the comparison with 2007 lidar data. Doing so would change their mass-balance results by about −0.03 m w.e. a⁻¹ . Reference Arendt, Luthcke, Larsen, Abdalati, Krabill and BeedleArendt and others (2008) used laser altimetry data from 2005 and 2007 and reported a mass balance of −2.78 ± 0.66 m w.e. a⁻¹, a value similar to the other previous studies.

Our results indicate ice loss significantly accelerated during the first decade of the 21st century for both Yakutat Glacier and for the YIF when compared to Reference Larsen, Motyka, Arendt, Echelmeyer and GeisslerLarsen and others (2007) and Reference Berthier, Schiefer, Clarke, Menounos and RémyBerthier and others (2010). The reasons for this increase in ice thinning include (1) a positive feedback mechanism, known as the Bodvardsson effect (Reference BodvarssonBodvardsson, 1955), where thinning lowers the surface elevation and exposes the ice to higher temperatures at lower elevations, causing accelerated ice loss, and (2) climate change. The town of Yakutat has seen a temperature increase of 1.3°C and annual precipitation increase of 1528 mm during the period 1948–2000 (Reference Larsen, Motyka, Arendt, Echelmeyer and GeisslerLarsen and others, 2007). During the last decade (2000–10), mean annual temperatures were 0.4°C higher, following the general trend of the 20th century. Increased temperature elevates the ELA and decreases the AAR, resulting in increased ice loss. The study by Reference Arendt, Luthcke, Larsen, Abdalati, Krabill and BeedleArendt and others (2008) covers the time period 2005–07, part of our study period. They compared NASA’s ATM data (2005) with University of Alaska laser altimetry data (2007) and found an area-averaged mass balance for Yakutat Glacier of −2.78 ± 0.66 m w.e. a⁻¹, 34% lower than what we found for the period 2000–07, which may reflect interannual variations. Additionally, this difference may result from different sources. While laser altimetry data collected along a glacier center flowline may not be representative for an entire glacier (Reference Berthier, Schiefer, Clarke, Menounos and RémyBerthier and others, 2010), this is not likely to be an issue in the case of the YIF as the glaciers show uniform surface lowering within elevation bands. However, monthly temperatures from the town of Yakutat reveal a 0.6°C lower mean annual temperature during the laser altimetry time period (September 2005 to August 2007) compared to 2000–07. Summer temperatures were comparable, but winter temperatures were lower. Precipitation did not show any trends, but the lower temperatures may have led to higher amounts of solid precipitation. Third, Reference Arendt, Luthcke, Larsen, Abdalati, Krabill and BeedleArendt and others (2008) did not include losses from the floating tongue. Our results (Table 2) indicate that this could account for an additional −0.5 m w.e. a⁻¹.

Reference Luthcke, Arendt, Rowlands, McCarthy and LarsenLuthcke and others (2008) found 11.6 ± 0.7 G ta⁻¹ of the mass loss from GRACE data (mascon region 10) for 2003–07. Mascon 10 includes the YIF as well as large glacier systems such as Malaspina Glacier and large parts of Glacier Bay. Our results indicate that 25% or 2.89 ± 0.03 G ta⁻¹ of the mass loss of this GRACE mascon came from the YIF.

The results of the five studies are summarized in Figure 7. We show corrected as well as uncorrected results for comparison. When we compared equal methods, we did not include adjustments for the floating tongue. Our results show significantly higher volume change rates than all previous studies.

Fig. 7.

Area-averaged mass balance for Yakutat Glacier for different years by various authors. The height of the box delineates the uncertainty of the value. Results from our study are depicted by a solid purple box (2000–07) and by a solid red box (2007–10) for DEM differences uncorrected for the floating tongue. Dashed boxes include corrections for the floating tongue in terms of ice loss (MB), and dotted boxes are corrected with respect to mass loss of the glacier–lake system (SLR). Earlier DEM differencing studies are shown in orange (Reference Larsen, Motyka, Arendt, Echelmeyer and GeisslerLarsen and others, 2007, 1948–2000) and in green (Reference Berthier, Schiefer, Clarke, Menounos and RémyBerthier and others, 2010, 1953–2006). The data from a laser altimetry study by Reference Arendt, Luthcke, Larsen, Abdalati, Krabill and BeedleArendt and others (2008, 2005–07) are shown in blue.

Partitioning of volume loss

Yakutat Glacier loses mass by both surface ablation and calving. Surface ablation is directly influenced by climate. However, dynamic adjustments of the glacier surface can also lead to changing surface mass balance, even under a constant climate. To illustrate this effect, the mean thickness change between 2000 and 2010 was −39 m. A mass-balance gradient of 0.0046 a⁻¹ (estimated from unpublished mass-balance data by the authors) results in a decrease in the surface mass balance of 0.18 m a⁻¹, due solely to this change in surface elevation. In contrast, ice loss from calving results from dynamic effects and is only indirectly linked to climate. At Yakutat Glacier, large calving events have been episodic in nature, with large tabular sections of the floating tongue periodically breaking away, interspersed with long periods (on the order of months to years) of relative quiescence. The terminus can then steadily advance until the next calving episode. Although tidewater glaciers experience similar patterns of calving retreat followed by slow advance, this periodicity occurs over much shorter time periods, usually days or weeks (Reference O’Neel, Echelmeyer and MotykaO’Neel and others, 2003; Reference Amundson, Truffer, Lüthi, Fahnestock, West and MotykaAmundson and others, 2008).

The long-term episodic nature of lake calving leads to a ratio of surface mass balance vs calving flux that fluctuates significantly with time. In our study, for the periods 2000–07 and 2007–10, calving accounted for 7.9% and 16.8% of the total mass loss respectively.

Comparison of Yakutat Icefield glaciers

Currently, two of the six glaciers of the YIF are exposed to calving dynamics: Yakutat Glacier (42% of the icefield) and Battle Glacier (18%). Yakutat Glacier has been a lacustrine glacier for at least a century (see Fig. 2, 1903), with the largest retreat of the YIF, whereas Battle Glacier has only recently become a lake-calving glacier, with almost no terminus retreat since 1903. The highest thinning rates (2000–10) are found on lake-calving Yakutat Glacier. Battle Glacier and land-terminating East Nunatak have the third and second largest thinning rates respectively (Table 1). The remaining land-terminating glaciers generally are thinning at lower but still significant rates. Yakutat, East Nunatak and West Nunatak glaciers have experienced terminus retreats exceeding 10 km since 1903. We note that they have all been exposed to calving during all or part of the last century.

Evolution and collapse of the icefield

Yakutat Glacier began retreating from its LIA maximum sometime during the 19th century, but the rate of retreat has accelerated since 1903 (Fig. 6). Total retreat between 1903 and 2010 was 15 km. Retreat rates have not been constant, possibly due to changing climate conditions, the episodic nature of calving at Yakutat Glacier, and lake geometry. Bathymetry (unpublished data by authors) shows a relatively shallow sill (150 m) across the lake at the narrowest part of the lake, compared to depths of 325 m at the 2010 terminus. The pinning of the narrows and shallower water may have inhibited calving, thereby helping to stabilize the terminus during the period 1960–80. This sill now entraps the large tabular icebergs that have recently calved from Yakutat Glacier from floating further down-lake (Fig. 6b).

The ice divide on the east branch of Yakutat Glacier is currently (2010) lower in elevation than on the west branch. In 1903 the opposite was the case, with the ice divide on the east branch at a higher elevation (Fig. 6a). The lowering of the east branch divide may be connected to tidewater glacier dynamics, since the ice divide is shared with West Nunatak Glacier. While it was a tidewater glacier, Nunatak Glacier could draw down ice faster, thus causing the ice divide to thin more rapidly on the east than on the west branch.

Our results clearly show that the entire YIF is in rapid decline. With little or no accumulation zones (AAR mostly <0.05), these glaciers are destined to continue their decline into the foreseeable future. Even if the current climate trends are reversed, it will take a substantial change in the regional ELA before these glaciers can begin growing again. We now address the question of how the YIF formed in the first place, and what then led to its collapse, by drawing on published glacial geology (e.g. Reference Barclay, Calkin and WilesBarclay and others, 2001), considerations of terrain and the IBC maps of 1903.

A ‘typical’ alpine glacier with zero mass balance will have an AAR value between 0.5 and 0.7 (Reference PatersonPaterson, 1994, ch. 3), with coastal Alaska favoring the latter value (Reference Meier and PostMeier and Post, 1962). The YIF itself does not have a high-elevation accumulation area. Thus, the original LIA YIF must have either been fed from nearby regions or been subject to a much colder climate or both. Events leading to the post-LIA collapse of the YIF must have preceded the first mapping of the region, because by 1903 the ice divides had already dropped to near the current ELA threshold (Fig. 6a), so that the AAR was probably well below that needed to sustain the glaciers. We suggest that the YIF is now a remnant icefield. Such remnants exist nearby in Glacier Bay (i.e. Burroughs Glacier) and also in Russell Fjord (Orange Glacier).

During the early 17th century, the east lobe of Hubbard Glacier (a major tidewater glacier to the northwest of Russell Fjord; Fig. 2) was at its maximum extent and spilled into the south end of Russell Fjord (Reference Barclay, Calkin and WilesBarclay and others, 2001). During the same period, Nunatak and Hidden Glaciers advanced into Russell Fjord, where they were then dammed by the east lobe of Hubbard Glacier. By the late 18th century, glacier ice had filled the entire southern part of Russell Fjord, with a terminus lobe advancing onto land beyond the south end of the fjord. Abetted by the generally cooler LIA climate, these circumstances could have led to the growth of the YIF: ice from Nunatak and Hidden Glaciers would have backed up because of the Hubbard dam, thereby increasing the height of the YIF ice divides and glacier elevations overall. Ice spilling over to the southeast could have fed the other branches of the YIF. By the end of the 18th century, the main and east lobes of Hubbard Glacier had retreated, and Nunatak Glacier became the primary source of ice into Russell Fjord. The retreat of Hubbard Glacier caused the ice-flow direction to reverse in the northwest arm of Russell Fjord. Ice started to retreat from the south end of Russell Fjord in the late 18th century (Reference Barclay, Calkin and WilesBarclay and others, 2001). Nunatak and probably Hidden Glaciers were tidewater glaciers at this time, and a calving retreat likely ensued with the waning of LIA climate conditions. Historically, in the early 1900s, East and West Nunatak Glaciers were still connected as one tidewater glacier calving into Nunatak Fjord (Reference Tarr and MartinTarr and Martin, 1914). However, rapid retreat eventually separated the two arms, with both retreating onto land. The changing climate and the retreat of Nunatak and Hidden Glaciers eventually led to the collapse and current condition of the YIF. Such a scenario is not without precedent: Glacier Bay is a prime example where LIA advance and expansion of the main trunk glaciers led to the formation of large peripheral glaciers and ice fields, which subsequently collapsed once the main trunk glacier retreated (Reference Larsen, Motyka, Arendt, Echelmeyer and GeisslerLarsen and others, 2007).

Other potential sources of ice for the growth of the YIF during the LIA are Art Lewis and Vern Ritchie Glaciers, which lie north of the YIF (Fig. 2). Both these glaciers have high-elevation accumulation areas and their growth during the LIA may have been sufficient to allow ice to spill over and feed Nunatak and Battle Glaciers (Fig. 2). Given the high precipitation rates in this region, the climate during the LIA may have been sufficiently colder to allow the YIF to grow. However, since the current ELA is essentially at or above the current ice divides, the difference would have to have been considerable if this was the only operative process. We also point out that growing ice fields are subject to a positive feedback effect, which would allow them to continue to grow, perhaps rapidly. This instability is similar, but reversed in sign, to what is currently happening.

Tidewater vs lacustrine glacier

Tidewater glaciers experience calving rates up to an order of magnitude greater than lake-calving glaciers, ice speeds are more than an order of magnitude higher and near-terminus surface slopes are steeper. In the following we propose a hypothesis to explain these differences.

We initially assume a temperate glacier in an over-deepened basin near its maximum extent in steady state, with the terminus exposed to calving. If the glacier experiences sufficient thinning, portions of the terminus area can become ungrounded. If the ungrounding allows a cavity to form, a tidewater system will likely react differently than a lacustrine system (Fig. 8). In a tidewater situation, a submarine cavity would rapidly be exposed to high basal melt rates, as water circulation driven by subglacial freshwater discharge would transport warm ocean water to the base of the ice. Measurements in Alaska (Reference Motyka, O’Neel, Connor and EchelmeyerMotyka and others, 2003b) and Greenland (Reference Motyka, Truffer, Fahnestock, Mortensen, Rysgaard and HowatMotyka and others, 2011) show that such melt rates can be well in excess of 1 m d⁻¹. Thinning due to subglacial melt then decreases the stability of the terminus and ice calves back to the grounding line. Indeed, floating termini are rarely observed in temperate tidewater glaciers, and, when present, appear to be a temporary and unstable feature (Reference Walter, O’Neel, McNamara, Pfeffer, Bassis and FrickerWalter and others, 2010). This rapid retreat then steepens the near-terminus surface slope, leading to increased extensional ice flow. Faster ice flow causes increased crevassing, which in turn helps drive calving rates (Reference Benn, Warren and MottramBenn and others, 2007). The glacier thus experiences high calving rates, high flow rates with large extensional gradients, and heavy crevassing. Higher velocities at tidewater glaciers are also facilitated by the denser water at their termini, which leads to lower effective pressures for a given ice thickness (Reference Van der VeenVan der Veen, 2002).

Fig. 8.

Positive feedback mechanisms when a glacier retreats into an overdeepened basin. As the glacier becomes ungrounded due to thinning, the density contrast between warm ocean water and fresh, cold subglacial runoff creates buoyancy-driven circulation in a tidewater system that results in submarine melting. This link (gray arrow) is broken in a lacustrine glacier system, because the freshwater density contrast will likely not be strong enough to trigger circulation, and water temperatures are too cold to cause subaquatic melting.

In the case of a lacustrine glacier, cavities formed by ungrounding can exist for an extended period of time. The subglacial discharge is not buoyant compared to the lake water, since the temperature and density differences are small. The lake water temperature in Harlequin Lake varies between 0.5 and 1.5°C, which appears to be typical of other proglacial lakes (Reference Boyce, Motyka and TrufferBoyce and others, 2007). These lower temperatures are a result of the lake being a closed system with icebergs in it. Thus, water circulation and heat exchange are generally minimal. Therefore, steep surface slopes do not develop and a positive feedback mechanism between retreat, surface slope, extensional thinning and crevasses is not established. The part of the glacier that is decoupled from its bed appears to be stable for an extended period of time. Indeed floating termini are commonly observed in temperate lake-calving glaciers. Lacustrine glaciers can form floating tongues that are stable for months to years or longer, whereas tidewater glaciers in the same climate are unable to maintain a floating terminus, which can lead to steeply sloped terminus areas and attendant high ice fluxes.

Eventually, continued thinning of a lake-calving terminus and lake-level rise can lead to episodic calving of large tabular icebergs, but these events may occur as infrequently as once a year. In tidewater systems, calving occurs much more frequently, often on a daily to weekly basis, abetted by tidal flexure as well as extensional thinning and crevassing.