Photogrammetric reanalysis of 1985 aerial photos has revealed substantial submarine melting of the floating ice tongue of Jakobshavn Isbræ, west Greenland. The thickness of the floating tongue determined from hydrostatic equilibrium tapers from ∼940 m near the grounding zone to ∼600 m near the terminus. Feature tracking on orthophotos shows speeds on the July 1985 ice tongue to be nearly constant (∼18.5 m d−1), indicating negligible dynamic thinning. The thinning of the ice tongue is mostly due to submarine melting with average rates of 228 ± 49 m yr−1 (0.62 ± 0.13 m d−1) between the summers of 1984 and 1985. The cause of the high melt rate is the circulation of warm seawater (thermal forcing of up to 4.2°C) beneath the tongue with convection driven by the substantial discharge of subglacial freshwater from the grounding zone. We believe that this buoyancy-driven convection is responsible for a deep channel incised into the sole of the floating tongue. A dramatic thinning, retreat, and speedup began in 1998 and continues today. The timing of the change is coincident with a 1.1°C warming of deep ocean waters entering the fjord after 1997. Assuming a linear relationship between thermal forcing and submarine melt rate, average melt rates should have increased by ∼25% (∼57 m yr−1), sufficient to destabilize the ice tongue and initiate the ice thinning and the retreat that followed.
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 In this paper we explore conditions that existed in the terminus region during its recent period of relative stability by examining two sets of high-elevation (∼13,500 m), high-quality aerial photographs of Jakobshavn Isbræ that were acquired two weeks apart during July 1985 [Fastook et al., 1995]. These historic photo sets have become increasingly important for documenting and understanding the dynamic state of this outlet stream prior to the rapid retreat and massive ice loss that began in 1998. The original photogrammetric analysis of this imagery is summarized by Fastook et al. . They derived a coarse Digital Elevation Model (DEM) over an area of approximately 100 km × 100 km by interpolation from several hundred positions determined manually from block-aerial triangulation and derived a number of velocity vectors by photogrammetric feature tracking. Prescott et al.  examined the terminus region more intensively and photogrammetrically determined surface elevations and motion vectors for about 500 crevasses on the floating ice, and adjacent grounded ice. Based on their analysis of strain rates and ice tongue thickness, Prescott et al.  estimated that the bottom melt rate along the base of the floating tongue was at least 109 m yr−1.
 The original negatives of the 1985 aerial photos, flown 10 July and 24 July, are archived at Mark Hurd Inc. (Minneapolis). We obtained 14 micron scans for our digital photogrammetric analysis. Details of the photogrammetric analysis are contained in the work by Motyka et al. . Estimated ground resolution for the images is ∼2 m [Fastook et al., 1995]. The master photogrammetric models cover much of the ablation area of JI and consist of three photo strips, each containing about eight photos with 60% along-flight overlap and about 20% cross-lap between strips [Motyka et al., 2010].
 We optimized photo contrast for glacier visibility and used BAE Socet Set (BAE-SS) digital photogrammetry NGATE software, optimized to perceive the glacier surface. The software program automatically weights the GCPs according to uncertainty to control the positions and orientations of the photos. The BAE-SS reported RMS model fit was <1 m. We then derived 20 m grid DEMs of the terminus region in UTM coordinates (Zone 22N) and with elevations referenced to WGS84 Ellipsoid. Photographic coverage of the terminus region involves only six photos (or four stereo pairs) of the 24 photos that were used for defining the overall photogrammetric model for JI. As such, our terminus DEM is a subset of a much larger DEM that appears in the work by Motyka et al. .
 We assessed the accuracy of the DEMs using various ground truthing data sets [Motyka et al., 2010]. These data sets are almost exclusively over land and include NASA ATM profiles and our own kinematic and static GPS surveys, performed during field campaigns in 2006–2009. The results of comparing elevations at ∼9000 points showed a Gaussian distribution with a standard deviation (σsd) = 2.8 m and a slightly negative bias (−0.7 m). Unfortunately, we lack ground truthing data for the 1985 ice surface in the terminus region. However, eight ice positions were surveyed farther upstream in 1985 and we estimate their accuracy at ±1 m. Comparison of these elevations (adjusted for ablation losses where needed) to our DEM yielded σsd = 2.4 m, very similar to our land results. Given these ice results and that the land points lie in close proximity to the ice margins (<5 km), we assigned an elevation uncertainty of ±2.8 m for the terminus ice surface DEMs.
 We generated orthophotos based on our DEMs and used the orthophotos for feature tracking and velocity determinations at 100 m grid points, using a modified form of IMCORR [Scambos et al., 1992]. The uncertainty of these velocities, based on degree of pixel correlation, is estimated at ±0.3 m d−1. We generated streamlines from the gridded velocity field using Matlab™ streamline function. These stream lines were then used to bound regions of the South Branch (SB) to analyze ice fluxes and submarine melt rates along the floating tongue.
2.3. Seawater Data
 A submerged moraine or sill forms a barrier between waters of Disko Bay and Kangia Ice Fjord (Figure 1). D. M. Holland et al. , based on relatively sparse data, reported the depth of this sill to be 250 to 350 m, but more recent multibeam surveys of the entrance sill indicate that the southern part is relatively shallow (∼100 m), whereas the northern part has a canyon with a depth of about 250 m (W. Weinrebe, personal communication, 2010). D. M. Holland et al.  reported that Kangia Ice Fjord itself is uniformly deep at ∼800 m, so that once over the sill, dense waters could in principle have an unobstructed pathway to the grounding line some 50 km inland, but their data are sparse.
 During the last three decades the Greenland Institute of Natural Resources (GINR) has collected conductivity, temperature, and depth (CTD) data at a station located in Disko Bay, about 5 km west of the village of Ilulissat and near the entrance to Kangia Ice Fjord (Figure 1). We used the data from this station to characterize Disko Bay waters that could potentially flow across the sill into the fjord. Casts were made on an annual basis at this station from 1980 to 2008 except for 1991–1993 and 1996. For 1991 and 1993 we used data from a station about 1 degree farther west. There are no data for 1992 and the closest station in 1996 was 4 degrees farther west. The date of occupation varied from year to year but was always in summer, between mid-June and late August.
2.4. Hydrostatic Equilibrium
 Our goal here is to determine the bottom topography of the floating tongue using the surface topography of our DEM. We chose the 24 July DEM over the 10 July DEM for this analysis because the 24 July aerial photos had slightly better surface definition. The first step is to adjust for voids created by crevasses. The resolution of our 20 m grid is sufficient to capture major crevasses, which are spaced about 100 m apart on the floating tongue and have depths of 20 to 30 m. The crevassed nature of the floating tongue is an inherited feature, advected from upstream of the grounding zone, where strong extensional strain rates exist. We applied an equal weight filter with a radius of 0.5 km to produce a smoothed surface. This procedure compensates for the voids created by crevassing, which is important when estimating hydrostatic equilibrium depths. We estimate the uncertainty in void space using this method at ±1 m freeboard. Note that we ignore any bottom crevassing on the ice tongue; the observed strain rates are so low that pervasive bottom crevassing is unlikely.
 Since our photogrammetry uses GCPs that are based on the WGS84 ellipsoid, our next step is to transform surface elevations to mean sea level (msl). We used the EGM96 geoid model for this conversion. These geoid corrections range from 28 to 29 m across our area of interest and are nearly linear. A check of the geoid correction against ATM data and our DEM at water level indicates a geoid model accuracy to ±0.5 m in our region. Correction for tidal stage was not made because the 24 July 1985 photos over the terminus were flown within 30 minutes of each other and when the tide stage was within 0.3 m or less of mean sea level. The latter was determined by using tide predication tables for the village of Ilulissat just outside the fjord, and an observed 10 minute phasing in tides between Ilulissat and the upper fjord in 2008 and 2009 (J. Amundson, personal communication, 2009).
 The next step is to calculate hydrostatic equilibrium ice depths from the ice freeboard (or ice height above mean sea level), Zf. We used the smoothed surface DEM of the floating tongue to represent Zf (x, y), where x and y are the DEM easting and northing coordinates, respectively. DEM freeboard ranges from ∼70 masl near the terminus to ∼110 masl near the grounding zone. Ice thickness H(x, y) is given by
where D is the distance from sea level to the bottom of the floating tongue and
Equation (2) requires assumptions about the density of glacier ice (ρi) and seawater (ρsw). We use 910 kg m−3 as an average density for the ice column based on findings of Lüthi et al.  in upglacier boreholes, and prescribe an uncertainty of ±5 kg m−3 (nearly pure ice to slightly “bubbly” ice). The density of seawater depends primarily on salinity but it is also a weak function of temperature and pressure. As we will discuss later, there is good evidence for circulation of seawater mixed with subglacial freshwater beneath the ice tongue. CTD data from the GINR oceanographic station near Disko Bay (Figure 1) indicates that seawater entering the fjord across the entrance sill during the mid-1980s had an average salinity of S = 34.1 and temperature T = 1.7°C (see Figure 5). The pressure melting point for S = 34.1 at 830 m depth (approximate depth at the grounding zone) is −2.5°C, so the thermal forcing is 4.2°C. We assume that subglacial freshwater discharge emerging from the grounding zone mixes with this seawater. The mixed water then forms a stratified layer directly under the floating tongue and becomes the buoyant medium for the ice tongue. Based on mixing ratios in waters emerging from submarine melting of tidewater glacier termini elsewhere (e.g., Alaska [Motyka et al., 2003], Petermann Glacier [Rignot and Steffen, 2008], and particularly fjords north of Jakobshavn [Rignot et al., 2010]), we assume that the mixed water has T ∼ 0.5°C and salinity, S = 31. Density ρsw at this T and S varies from 1027.3 kg m−3 at 500 m depth to 1028.7 kg m−3 at 800 m depth.
 Salinity is the primary source of uncertainty in ρsw calculations. The effect of depth on density is quite small: ρsw varies by only 0.005 kg m−3 per m of water depth for our range of values. For temperature, ρsw varies by less than 0.1 kg m−3 per 1° C. In contrast, a change in salinity of 1 corresponds to a change of 0.8 kg m−3 in density. For example, if we assume an uncertainty in salinity of ±3, the uncertainty in D would be ±10 m for D = 500 m and ±16 m for D = 800 m.
2.5. ATM Data
 We use NASA ATM flights of Jakobshavn Isbræ to assess changes to the ice tongue after 1985. We acquired these data sets as “blocks” or platelets from W. Krabill (personal communications, 2008, 2009) and used the easting and northing flight line coordinates of each tile to interpolate our 1985 DEM to determine changes in surface elevations. The coordinates provided for each tile are the center point average of ∼900 laser returns within a square of ∼40 m, which is twice the grid size of our DEM. Repeat ATM lines were also differenced to assess changes between flights. The first ATM flights over the terminus were conducted in 1993 and approximately followed the south branch (SB) centerline (see Figure 7). Subsequent flights of SB were over the north edge of the ice stream in 1997, 1998, and 2001 and a cross profile at 546 km easting (UTM zone 22N) in 1997. ATM data is also available for a portion of the north branch (NB) on a nearly annual basis from 1993 to 2001 [Thomas et al., 2003]. The reported accuracy of the ATM data is ±0.3 m [Krabill et al., 2004].
2.6. Propagation of Uncertainties
 Sources of error in our calculation of hydrostatic equilibrium thickness of the floating tongue include uncertainties in ρi (±5 kg m−3), ρsw (±2.4 kg m−3), DEM model bias (±0.7 m), geoid (±0.5 m), and estimating crevasse void space (±1 m). In addition, there is a random uncertainty [cf. Rolstad et al., 2009] in our DEM elevation determinations of σr = ±2.8 m. However, the radius of 0.5 km that we used to smooth the surface effectively averages out this random error and we therefore do not include it in our propagation of uncertainty. The remaining uncertainties in model bias, geoid, and void space are systematic uncertainties that affect Z (x, y), the surface elevation in our DEM used to define freeboard and consequently D from equation (2). Propagation of these uncertainties leads to a standard error of σZ = ±1.3 m for the surface elevation of our DEM.
 Uncertainties in ρi and ρsw affect the buoyancy of the ice column. Propagation of these uncertainties with the uncertainties in Z(x, y) leads to a relative error of ∼5% for ice thickness H (x, y). For ice near the terminus of the floating tongue (where H ∼ 590 m), this translates to σH = ±30 m; for ice near the grounding zone (Hi ∼ 930 m), σH = ±45 m. Uncertainties in seawater density affect the thickness calculation systematically, but by varying amounts (more where ice is thicker). However, they have a negligible effect on the general tongue geometry: for example, a 15 m uncertainty in the difference between terminus and grounding zone thicknesses equates to a fraction of a degree in slope change over the 9 km length of the floating tongue.
3.1. Topography and Velocity
 A shaded relief image with a 50 m interval contour overlay based on the 24 July 1985 20 m grid DEM is shown in Figure 2. The results of the velocity analysis are displayed in Figure 3, overlaid on the orthophoto for 24 July. Our speeds are in excellent agreement with ground-based optical surveys of targets on the tongue reported by EH and ECH but are slightly faster than previously reported photogrammetric results [Pelto et al., 1989; Fastook et al., 1995]. The latter may be a consequence of our much higher-resolution DEM, which allows better registration of orthophotos and therefore the terminus velocity field. Streamlines derived from the velocity field are also shown in Figure 2.
 The 1985 ice flow pattern for the South Branch (SB) shows speed increasing as ice flowed into the grounding zone (GZ), reaching a maximum of 19.7 m d−1 (Figure 3b) (see Figures 2 and 4 for location of GZ). Ice speed then slowed to 18.5 m d−1 on the ice tongue and was essentially constant for the next 8 km with negligible longitudinal strain rates (Figure 3b). In the last kilometer before the calving front, speed reached 21.4 m d−1. The dominance of the 1985 SB outlet glacier is clearly evident in Figures 2 and 3.
3.2. Grounding Zone
 We use the term “grounding zone” (GZ) (following arguments of EHC) and estimate its position to lie between 549.5 km and 550.0 km easting UTM (Figure 2) based on several arguments. The average ice thickness of the SB at 549.5 km (discussed later) is ∼930 ± 40 m, which is consistent with iceberg measurements related to full-ice-thickness calving events in 2008 (900 ± 50 m [Lüthi et al., 2009]) and other calving events that occurred in this general vicinity during 2007 and 2008 [Amundson et al., 2008, 2010]. This thickness is also consistent with soundings made by D. M. Holland et al.  in the proglacial area (cyan dots in Figure 2), which exceeded 800 m in depth. Bed depths slightly greater than 800 m are also consistent with ice cliff heights determined from our various field surveys during 2007–2009. Another indicator of grounding zone position is the change in velocity: SB ice velocity first increases and then decreases in the region around 550 km (Figure 3). Such changes are consistent with numerical models for changes in speed across a grounding line [Goldberg et al., 2009; M. Lüthi, personal communication, 2009]. Finally, this position for the grounding zone can be distinguished in a comparison of elevation changes between 1985 and 2007 [cf. Motyka et al., 2010, Figure 6]. Our position for the GZ differs from Thomas et al. , who placed it ∼2 km farther upstream, and Csatho et al. , who placed it ∼2 km farther downstream.
3.3. Bottom Topography of the South Branch
 Here we focus on the 1985 bottom topography of the SB outlet glacier, which drained the majority of the Jakobshavn Isbræ basin and contributed ∼80% of the ice entering the floating tongue. We chose for detailed topographic analysis a ∼3 km wide, 10 km long section of the SB extending from 541 km to 551 km easting (see Figure 2 for boundaries). The west boundary for this “ribbon” of floating ice is defined by the location of the calving zone; the east boundary by the GZ. Shear zones along the fjord walls pose problems because ice flexure associated with buttressing effects can prevent ice from achieving full hydrostatic equilibrium [Lingle et al., 1981]. Our velocity map indicates that the south wall shear zone extends for ∼1 km from the south wall grounding line (Figure 3) and we therefore positioned the south boundary of the ribbon accordingly. This boundary also avoids problems with the topographic feature labeled “Rumple” (ECH), where we know bedrock is quite shallow and the ice is not in hydrostatic equilibrium. The shear zone on the north side is more complicated and much wider (ranging from 1–2 km from the north wall grounding line). We placed the ribbon boundary south of this zone: it roughly coincides with a region called the “zipper” (ECH), which is the juncture of ice flow from the two main branches (Figure 2). Our choices are in accord with field measurements by Lingle et al. , which indicated that the floating tongue was fully responsive to tidal flexure at distances of about 1–1.5 km or more from the north wall. Our choice of boundaries also avoids other ice margin problems associated with our smoothing of the surface terrain.
Figure 4 displays the SB bottom topography based on the assumption of hydrostatic equilibrium, using our smoothed surface DEM. Our choice of a “smoothing” distance was a compromise: it needed to be long enough to smooth out crevasse fields but also short enough not to average out interesting bottom features. Small bottom features cannot be resolved, because they are not expressed at the surface, but larger features manifest themselves in the surface elevations in a “smoothed” or “blurred” manner [Rignot and Steffen, 2008]. Despite the qualitative nature of Figure 4, our analysis reveals the existence of a large “channel” incised into the bottom of the ice tongue. This channel emanates from the deepest part of the grounding zone, in the center of the SB, and continues to the terminus along the center flow line. The smoothing process has likely made the channel appear wider and shallower than it is in reality. There is also a “natural filter” at work here, that is, a narrow deep channel would not reveal itself as such on the surface given the thickness of ice. Nevertheless, we can reasonably state that the channel is at least a couple of hundreds of meters in width and several tens of m in depth.
3.4. Seawater Data
Figure 5 displays the temperature and salinity data obtained from the GINR CTD casts at Station 26 in Disko Bay near the entrance to Kangia Ice Fjord (Figure 1). The data are similar to those used by D. M. Holland et al. [2008, Figure 3], but with additional data from the mid-1990s. Our presentation of the data as a time series for this station differs from D. M. Holland et al.  in order to provide details of temporal temperature and salinity changes. We also included data for 1991 and 1993 from a station 1° farther west to fill in the data gap. Temperature data for the uppermost part of the water column in 1993–1995 are variable and appear to reflect local circulation effects; we therefore did not include them in Figure 5.
 The deepest and warmest water (at 300–350 m) averaged 1.7°C during the 1980s. Despite data gaps, there appears to have been a distinct cooling trend during the mid-1990s. The record then shows that a significant and sustained increase in seawater temperature occurred at all depths by 1997 (also reported by D. M. Holland et al. ). Temperatures of deep water (300–350 m) averaged 2.8°C between 1997 and 2008, an increase of 1.1°C with respect to the 1980s decadal average. Salinity of the deep waters also increased slightly.
3.5. The Floating Tongue and Submarine Melting
 In this section we discuss methodology for estimating the rate of submarine melting along the SB flow band of Figures 2 and 4. The geometry of the floating tongue together with the very low strain rates (Figure 3) indicate that large amounts of ice must be lost to melting by ocean water. For example, the ice that was at the GZ a year prior to the image acquisition has thinned by over 200 m while traversing an area of near zero strain rates and negligible lateral spreading (Figure 3). To investigate the pattern of melting more closely, we integrate the continuity equation along the flow band. Here we assume that the velocities on the floating tongue are constant with depth, so that surface velocity is equal to the depth average. As a column of ice with thickness h traverses the GZ and is exposed to ocean melt, it experiences thickness change:
where dh/dt is the rate of thickness change of a given ice column (in the Lagrangian sense), ∂h/∂t is the thickness change at a given map location (in the Eulerian sense), the last two terms are advective terms that relate the two, x and y are the along-flow and cross-flow coordinates, and u and v are the respective velocity components. We can now use the mass continuity equation
where qx = hu and qy = hv are the ice fluxes, and is the melt rate, which incorporates both surface and bottom melt. Equation (3) then reduces to
where and are the longitudinal and lateral strain rates. Equation (5) can be integrated to obtain the average melt that an ice column has experienced since crossing the GZ at time t = 0,
The time T can be related to the position x along a central flow line by integrating the velocity along the flow line,
The angled bracket for the melt rate represents the average melt rate that a given column of ice has experienced; it is thus a combination of a spatial and temporal average. In practice, we computed equation (7) along flow lines spaced 100 m apart within the flow band shown in Figure 2. We then averaged the melt rate at each x along the flow band to produce Figure 6.
 An essentially equivalent method is to use flux gates at the GZ and x, and integrate q across the width of the flow band at GZ and x. The average melt rate at the exit gate for the time interval for ice to travel between flux gates is then given by
where A is the planar area of the flux band between the gates and ΔQ is the difference in flux between the entrance and exit gates. The two methods gave nearly identical results.
 The resulting melt distribution is shown in Figure 6. This includes an estimated surface melting contribution of 4 m yr−1 (ECHB), which is more than an order of magnitude smaller than the total derived melt rates. The time axis in Figure 6 shows the date when ice at each position had crossed the “grounding line” entrance gate, which we have chosen to be stationary at x = 549.5 km in part to simplify analysis. We also chose this position because it is sufficiently removed from the actual GZ so that hydrostatic equilibrium is not an issue and the assumptions in calculating ice thickness are valid.
 We have neglected changes in the velocity field for this analysis. This is justified by observations by EH who measured velocities from August 1984 to October 1986 and found no seasonal velocity variations exceeding measurement errors (0.75 m d−1, or 4%). We also use the absence of such velocity variations to argue that no significant changes in ice thickness occurred during the year preceding this analysis. When the floating tongue did thicken in the early 1990s, it had an immediate dynamic effect: A thickening of ∼11% (concentrated near the GZ, discussed below) resulted in a slowdown of also ∼11%. The absence of such a slowdown (or speedup) in 1984/85 indicates that seasonal changes in geometry did not have a great effect on our melt rate calculation.
 We assume a thickness uncertainty of 30 m for ice transiting the GZ before 24 July 1985 based on linear scaling of EH's estimate of uncertainty in their seasonal velocity variations (4%). The uncertainty bounds shown in Figure 6 are based on this estimate plus uncertainties in velocities and the relative uncertainty in ice thickness difference, which ranges from ∼2 m at 549 km E to 15 m at 541 km E.
 We truncated the melt rate curve at x = 548 km because uncertainties closer to the entrance gate become too large. These uncertainties increase because small changes in the flux across the grounding line affect the local melt rate calculation most. Our degree of confidence increases progressively with distance away from the entrance gate (Figure 6). For the period between the summers of 1984 and 1985 (which is equivalent to a distance of ∼7–8 km from the GZ), the melt rate is 228 ± 49 m yr−1 (0.62 ± 0.13 m d−1) (Figure 6 and Table 1). Calving, submarine melting, and surface ablation account for roughly 70, 29, and 1% of ice losses from the SB floating tongue during this period.
Table 1. Annual Melt Rate for 24 July 1984 to 24 July 1985
Net ice loss (km3 yr−1)
4.42 ± 0.94
Surface ablation (km3 yr−1)
0.08 ± 0.01
Submarine melt rate (km3 yr−1)
4.34 ± 0.94
Average melt rate (m yr−1)
228 ± 49
Average melt rate (m d−1)
0.62 ± 0.13
 The average melt rates reflect both the seasonal cycle as well as any other temporal and spatial variations in melting patterns that a particular ice column may have experienced during its travel. Ice near the entrance gate in Figure 6 has only experienced summer conditions, when buoyancy driven convection is much stronger. Spatially, melting and convection would also be expected to be most intense at and near the GZ. The calculated melt rates do support this idea but the uncertainties are large: see x = 548 km in Figure 6 (1.5 ± 0.7 m d−1). In contrast, ice at 542.75 (1 year away) has gone through both temporal and spatial variations. The former is related to high melting in summer and low melting in winter, while the latter is related to a possible decline in melt rates as the ice advects away from the entrance gate. This spatial change in melt rate would be the result of the cooling of convected waters as they travel outward beneath the ice tongue and incorporate ice melt and the reduced thermal forcing as the freezing point of water increases with decreasing pressure.
3.6. Post-1985 Surface Elevation Changes
 Elevation changes between the 1985 DEM and ATM data (see Figure 7 for location of profile lines) are shown in Figures 8–11. These profiles are mostly over floating portions of the terminus, thus small changes in surface elevation can reflect significant changes in overall ice thickness.
 Only one ATM line was flown over SB prior to 1998 (line SB flown on 9 July 1993) (Figure 7). Comparison of that line to the 24 July 1985 surface reveals little change along most of the path, except at the terminus and in the region near the GZ, where elevations increased by an average of 11% (Figure 8). This thickening coincided with a decline in tongue velocity from ∼18 m d−1 to ∼16 m d−1 [Joughin et al., 2004; Luckman and Murray, 2005]. The next flights were not until mid-May of 1997. A transverse profile transects the tongue at 546 km easting, about half way between the GZ and the terminus (line T in Figure 7). Elevations increased by up to 20 m on either side of the SB between 1985 and 1997, in regions that are known to be grounded or over a shear zone margin (Figure 9). As previously discussed, changes in the shear zones are not amenable to interpretation in terms of hydrostatic equilibrium because of buttressing effects. What is interesting is that elevations over the SB flow band of Figure 4, where ice is in hydrostatic equilibrium, did not significantly change.
 Line NB, which crosses a section of the NB floating tongue (Figure 7), had the greatest frequency of flights during the late 1990s and changes that occurred along this flight line have been reported by Thomas et al.  and Csatho et al. . Here, we focus on the tongue and terminus portion of the flight line (Figure 10). Ice elevations there gradually increased by a few meters during the first part of the 1990s but then dropped by ∼6 m yr−1 between 1997 and 1998 with the rate of surface lowering increasing to ∼10 m yr−1 in succeeding years.
 We next examine Line Z (Figure 7), an ATM path flown on 13 May 1997 and then again in midsummer in 1998. The path goes over the east part of the SB, the “Zipper” and then up a steep ridge. Terminus fluctuations are clearly evident in Figure 11 with an advance of ∼2 km between 1985 and 1997 followed by an abrupt retreat of over 4 km during 1997–1998. The apparent 1985–1997 advance may be partly attributable to the 2 month seasonal difference. However, the ice surface also increased in elevation at a rate of ∼2 m yr−1 in the region between 545 km easting and the base of the steep ridge. In contrast, the surface dropped at rates of up to 5 m yr−1 between 1997 and 1998. An ATM line was flown on 27 May 2001 (line Z′ in Figure 7) but it is not directly comparable to 1997 and 1998 because the path lies about 300 m north of line Z. However, a comparison to the 1985 DEM surface is shown in Figure 11 (dotted lines). To derive an approximate rate of change in surface elevation between 1998 and 2001, we assumed that the ice surface in 1998 was at least as high as in 1985. (This assumption is based on a comparison of 1985 to 1998 profiles along the neighboring flight path Z.) The average change between 1998 and 2001 from Figure 11 is ∼−5 to −6 m yr−1; we consider these rates to be minimum estimates as the 1998 surface is likely to have been somewhat higher than our assumption.
3.7. Post-1985 Changes in Melt Rate
 Given that submarine melting accounted for ∼29% of ice loss along the SB floating tongue during the mid-1980s, it is reasonable to assume that any significant change in seawater temperature would correspondingly affect the ice balance of the floating tongue. The GINR CTD station near the mouth of the Kangia Ice Fjord and post-1985 ATM data allows us to evaluate the effects of changing seawater temperatures. The entrance sill at the mouth of the fjord forms a barrier to waters entering the fjord from Disko Bay. The sill is ∼250 m at its deepest part (Weinrebe, personal communication, 2010). Provided that there is no other obstruction up-fjord to impede flow, dense waters could in principle have an unobstructed pathway to the floating tongue and GZ some 50 km inland [D. M. Holland et al., 2008].
 Our estimate of the 1984–1985 annual melt rate (Table 1) serves as a starting point for evaluating subsequent changes. We consider this melt rate to be representative of the Jakobshavn system during the 1980s based on the following factors: (1) the terminus remained in a relatively stable position during this period [Sohn et al., 1998]; (2) the velocity on the floating tongue remained essentially constant from 1961 to at least 1986 [Pelto et al., 1989]; and (3) seawater temperatures at Station 26, although showing some oscillation, showed no significant long-term change between 1980–1990. As discussed in section 3.6, the first signs that the floating tongue was thickening came from 1993 ATM data (Figures 8 and 10), which was the first time that ATM was flown over JI. Thickening of the floating tongue continued into 1997 (Figures 10 and 11). In contrast, land terminating regions of the ice sheet immediately north and south of the floating tongue experienced significant thinning during this same period [Motyka et al., 2010]. In view of this observation, the thickening of the floating tongue is unlikely to have been caused by an increase in glacier surface mass balance. Instead, we suspect that the thickening was a response to a change in ocean-glacier interactions, that is, a decline in bottom melting of the tongue.
 Although there are gaps in the seawater temperature record for the period 1991–1996 at Station 26, inclusion of data from the station farther west indicates that there was a drop in deep seawater temperatures, perhaps by as much as 0.5°C or more, that lasted for several years during the mid-1990s. This drop in temperature would have decreased the amount of thermal forcing, thereby reducing the bottom melt rate and allowing the floating tongue to thicken. If we decrease thermal forcing by 0.5°C and assume a simple linear relationship between thermal forcing and submarine melt rate (justified if subglacial meltwater discharge is the primary force driving convection [cf. P. R. Holland et al., 2008; P. R. Holland, personal communication, 2009], then melt rates should have decreased by ∼12% during the mid-1990s. This corresponds to a drop of ∼25 m yr−1 with respect to our derived 1984–1985 melt rates. The corresponding change in freeboard is ∼3 m yr−1, which is consistent with the observed thickening during the mid-1990s (Figures 10 and 11). Unfortunately, the record of ATM elevation changes over the SB floating tongue between 1985 and 1997 is too sparse for a more conclusive statement. As discussed earlier, the thickening during the mid-1990s coincided with a decline in tongue velocity from ∼18 m d−1 to ∼16 m d−1 [Joughin et al., 2004; Luckman and Murray, 2005].
 The temperature record at Station 26 (Figure 5) shows seawater temperatures increased significantly at all depths after 1997. Using the increase in seawater temperatures of ∼1.1°C for bottom waters and again assuming a simple linear relationship between thermal forcing and submarine melt rate then melt rates would have increased by ∼25% after 1997 with respect to our derived 1985 melt rates. Applying this change to our area-average melt rate in Table 1 gives an increased melt rate of ∼57 ± 12 m yr−1 for the SB.
 Although NASA ATM flights over the Jakobshavn floating tongue are sparse for the 1990s, they nevertheless do provide evidence for thinning rates that are in accord with our estimates of disequilibrium melting. The equivalent change in freeboard for a disequilibrium melt rate increase of 57 m yr−1 would be ∼−7 m yr−1, a rate that would be readily detectable from repeat ATM flights. Flight line NB had the highest frequency of flights but crossed just a portion of the floating tongue. The assumption of hydrostatic equilibrium is most reliable for the section from 541 to 545 km easting, before the flight line enters the shear zone and grounded ice (see Figure 7; labeled “floating” in Figure 10). The change in freeboard for this section averaged ∼−5.5 m yr−1 during 1997–1998 then increased to ∼−10 m yr−1 during 1998–2001. These values compare well, given the uncertainties, with the expected average change in freeboard, although the rate of thinning after 1998 may have been influenced by acceleration and dynamic thinning.
 We next examine ATM lines Z and Z′ (Figure 11). These paths traversed the leading edge of the SB then continued over the “Zipper” (see Figure 7). For the period 1997–1998, the change in freeboard varied considerably along line Z but was most pronounced near the terminus, where it was ∼−5 m yr−1, again similar to the rate expected from our linear assumption. There was little or no change in freeboard along the central part of this path but the change in freeboard was again ∼−5 m yr−1 farther upstream as the flight line approached the ridge between the south and north branches. The change in freeboard ranged between ∼−5 and −8 m yr−1 between 1998 and 2001, along line Z′. Actual change may have been higher, given our conservative assumptions on the 1998 ice surface as discussed above.
4.1. Summary of Findings
 We begin our discussion by summarizing our findings.
 1. The thickness of the SB floating tongue tapered from ∼940 m near the GZ to ∼600 m near the calving front in late July 1985 (Figures 4 and 6). Given that there is little or no evidence for dynamic thinning, the change in thickness must be related to melting.
 2. The average annual submarine melt rate between the summers of 1984 and 1985 was 228 ± 49 m yr−1 (0.62 ± 0.13 m d−1) (Table 1).
 3. Our analysis of hydrostatic equilibrium depths revealed the existence of a large channel incised into the sole of the floating tongue (Figure 4).
 4. CTD data from GINR Station 26 in Disko Bay, located just seaward of the barrier moraine at the mouth of Kangia Ice Fjord, documented significant changes in seawater temperatures on decadal and subdecadal scales. These data include measurements made during the 1990s that were not reported by D. M. Holland et al. .
 5. Comparison of ATM data to our 1985 DEM and ATM ice elevation changes over the floating tongue showed thickening of ice during the mid-1990s followed by progressive thinning after 1997. Using Station 26 CTD data and assuming a linear relationship between thermal forcing and submarine melting, we found that changes in the degree of submarine melting are consistent with observed elevation and thickness changes.
4.2. Causes of Submarine Melting
 The submarine melt rates at JI are surprisingly high but are consistent with recent findings of Rignot et al.  in fjords to the north of JI. We believe that the direct cause of these high rates of melting at JI is the circulation of warm seawater that is brought into contact with the bottom of the ice tongue through buoyancy driven convection of subglacial freshwater discharge from the grounding zone (Figure 4), similar to convection-driven submarine melting of tidewater glaciers in Alaska [cf. Motyka et al., 2003] and in Greenland [cf. Rignot et al., 2010; Rignot and Steffen, 2008]. Warm seawater enters Kangia Ice Fjord from Disko Bay across a ∼250 m deep sill. Once inside the fjord they can circulate to the floating tongue and GZ if the pathway for these waters is unobstructed [D. M. Holland et al., 2008]. The channel shown in Figure 4 was likely incised into the ice by bottom melting caused by this circulation. The channel location at the deepest and central part of the grounding zone is consistent with the exit of a large subglacial stream from the grounding zone. In addition, Pelto et al.  and EH both reported regions of strong upwelling of turbid water along the terminus at approximately the same location where our analysis indicates that the channel exited at the terminus.
 Based on an analysis of surface melting and frictional and geothermal melting at the base, EH estimated the subglacial freshwater discharge at the GZ to be 750–1500 m3 s−1 in summer and 64–105 m3 s−1 in winter. We believe that the magnitude of this discharge coupled with thermal forcing of 4.2°C at the grounding zone combined to produce the observed high rates of melting. The circulation along the base of the ice tongue is likely driven by buoyancy. Strongest melting would occur during the summer when subglacial discharge would be greatest. A decline in thermal forcing also occurs as the mixed water ascends in elevation, resulting in a corresponding decline in average melt rate (Figure 6).
Rignot and Steffen  inferred submarine melting rates of up to 25 m yr−1 beneath the 60 km long ice tongue of the Petermann Glacier in NW Greenland, an order of magnitude less than found for JI in our analysis. Reasons that might explain this difference in melt rates include (1) thermal forcing at JI is nearly double that of Petermann, (2) surface ablation is substantially higher (4 m yr−1 versus 1.2 m yr−1), and (3) the JI drainage basin is considerably larger. Both points 2 and 3 are expected to lead to more vigorous buoyancy driven convection and hence higher rates of heat transfer to the ice. Using radio echo sounding (RES), Rignot and Steffen  also detected substantial meltwater channels incised into the bottom of the floating tongue, similar but better defined than the channel we inferred at JI from our hydrostatic equilibrium analysis.
 Our rates are also twice as large as estimated by Prescott et al. . We believe the reasons for this difference are related to our much better controlled and defined DEMs, orthophotos, and velocity fields plus our much more thorough analysis of hydrostatic equilibrium and dynamic thinning. Prescott et al.  also showed the problems involved in calculating strain rates in this zone of severe crevassing. Our method of using flux gates (essentially the integrated form of the mass continuity equation) avoids such problems.
4.3. Triggering of Current Instability
 A major destabilization of the terminus was clearly initiated during the summer of 1998, as evidenced by glacier thinning, retreat, and speedup [Thomas, 2004; Joughin et al., 2004; Luckman and Murray, 2005]. This destabilization progressively increased in magnitude in subsequent years and continues today. Here, we discuss the probable trigger for these dramatic changes. D. M. Holland et al.  showed that an upwelling of deep warm ocean waters associated with the Irminger Current migrated up the west coast of Greenland, reaching Disko Bay by 1997 and hypothesized that this current was the cause of the observed increase in seawater temperature at Station 26 (Figure 5). D. M. Holland et al.  also proposed that as a result, warmer waters entered Kangia Ice Fjord across the sill and induced an increase in basal melt rate, thereby causing the subsequent breakup of the floating ice tongue. Our work provides strong evidence in support of this hypothesis and also provides the driving mechanisms by which this submarine melting occurs. We note that a similar process may have occurred at Helheim Glacier in Sermilik Fjord, east Greenland [Straneo et al., 2010].
 As previously mentioned, given that submarine melting accounted for ∼29% of ice loss along the SB floating tongue during the mid-1980s, it is reasonable to assume that any significant change in seawater temperature and/or meltwater discharge would correspondingly affect the ice balance of the floating tongue. Based on our analyses, we estimate that the average annual submarine melting could have increased by ∼57 m yr−1 after 1997 and therefore, easily acted as the initial trigger for destabilizing the floating tongue. As the tongue thinned, it became decoupled from its mooring on stabilizing features. Upstream, the SB progressively accelerated, by 30% between 1998 and 2001, leading to increased dynamic thinning of ice entering the fjord tongue. This combination of melting and dynamic thinning eventually caused the total disintegration of the floating tongue and led to the glacier's current status as discussed by Thomas  and D. M. Holland et al. . The pattern of acceleration caused by thinning, retreat, and upstream propagation is in accord with the tidewater glacier instability discussed by Pfeffer .
 The period of retreat and acceleration coincided with a gradual and slight increase in air temperatures and the number of positive degrees days [Thomas, 2004; Csatho et al., 2008; D. M. Holland et al., 2008] and an upward migration of the melt zone on the Greenland Ice Sheet [Steffen et al., 2004; Hall et al., 2008]. These higher temperatures and increased surface melting would have led to higher rates of subglacial discharge, which in turn enhance submarine convection and help drive the melting of the floating tongue. An increase in basal sliding triggered by an increase in surface water propagating to the glacier bed is unlikely to have been the cause of the initial destabilization, as was pointed out by Joughin et al.  at Jakobshavn Isbræ and by Nick et al.  at Helheim Glacier (east Greenland).
 The bottom topography of the July 1985 floating tongue was obtained using high-resolution DEMs and assuming hydrostatic equilibrium. We used values for ice and seawater densities and other parameters that are in good agreement with upstream borehole studies and Disko Bay CTD data. The resultant topography shows a conspicuous channel incised into the bottom of the floating tongue that we believe to be the result of buoyancy driven convective melting. Our conservative estimate for the position of the 1985 grounding zone is between 594.5–550.0 km easting UTM.
 Velocities derived from orthophotos in conjunction with ice thickness allowed estimates of melt rates using ice fluxes. Velocities were essentially constant over most of the 10 km long 1985 floating tongue and dynamic thinning was negligible except near the terminus. The average submarine melt rate between the summers of 1984 and 1985 is surprisingly high: 228 ± 49 m yr−1 (0.62 ± 0.13 m d−1). The summer average is likely even higher (≥1.5 m d−1) but the uncertainties are large.
 We believe that the direct cause of these high rates of melting is the circulation of warm seawater that is brought into contact with the bottom of the ice tongue. The driver for this circulation is the buoyant convection of subglacial freshwater discharge from the grounding zone. Given the relative stability of seawater temperatures in Disko Bay between 1980 and 1990, bottom melt rates were probably relatively constant during this period. Using a simple linear relationship, we propose that a 1.1°C increase in seawater temperature that occurred by 1997 caused the melt rate to increase by ∼57 m yr−1. Changes in freeboard determined from post-1997 repeat NASA ATM flights are in good agreement with our estimate of disequilibrium melting. We therefore conclude that the direct cause of destabilization of the floating tongue was the significant increase in bottom melting due to an increase in seawater temperature as proposed by D. M. Holland et al. .
 In summary, our photogrammetric analysis shows that Jakobshavn Isbræ's floating tongue was subject to large submarine melt rates well before its recent retreat. A subsequent increase in ocean temperatures, caused by an incursion of warm and saline water [D. M. Holland et al., 2008] appears to have thinned the floating tongue to below a critical threshold and led to its disintegration and a dramatic increase in ice flow velocities [Thomas et al., 2003]. Outlet glaciers in contact with seawater can therefore react very strongly and rapidly to changes in ocean conditions, confirming conclusions by Motyka et al.  for southeast Alaska and by D. M. Holland et al.  for west Greenland. Understanding and predicting rapid glacier changes requires a careful study and monitoring of proglacial fjords and a better understanding of ice-ocean interaction.
 H. Brecher generously provided us with his survey data for photo control points and data from his original photogrammetric models. We thank M. Lüthi, J. Amundson, D. Podrasky, and J. Brown for assistance with field work and helpful discussions. The manuscript was greatly improved by comments from the associate editor and three anonymous reviewers. The SPOT5 image used for the 2007 terminus position was provided by the SPIRIT Program. Funding was provided by NASA's Cryospheric Sciences Program (grants NNG06GB49G and NNG06GA44G) and the Danish Agency for Science, Technology and Innovation. Additional support was provided by the Geophysical Institute, University of Alaska, and the Greenland Institute of Natural Resources.