Grounding line migration and high-resolution calving dynamics of Jakobshavn Isbræ, West Greenland

Abstract

[1] We performed three field campaigns in 2004, 2007, and 2010 at the southern margin of the Jakobshavn Isbræ, West Greenland, in order to infer flow velocities and their changes from photogrammetric time-lapse imagery with a temporal resolution of 20 min and a spatial spacing of about 30 m on the glacier surface. Area-wide analysis of more than 3000 three-dimensional trajectories at individual glacier positions allow for both the mapping of the grounding line and the detailed observation of flow variations during major calving events. From 2004 to 2010, the grounding line of Jakobshavn Isbræ retreated 3.5 ± 0.2 km. Considering previously published results, the grounding line retreat amounts to 6 km since 1985. The glacier has an ephemeral floating tongue that can establish during the readvance of the glacier front and break apart after large calving events. Observations of a major calving event show that an acceleration of flow velocities coincides with the onset of the break up during which flow velocities of up to 70 m/d can be reached. Moreover, large vertical displacements of the glacier front in the order of 15 m and lowering of 8 m at positions 500 m beyond the calving front were observed 2 days before the calving event. After the break up, the glacier slowly adjusts to the new boundary conditions within the next 4–5 days. Flow velocity variations caused by calving were detected up to 1 km upstream only which indicates that individual calving events have no immediate effect on the large-scale glacier dynamics.

Key Points

• Development of a method to determine the location of the grounding line
• Inland migration of the grounding line of Jakobshavn Isbrae
• Observation of high-resolution flow pattern during calving event

1 Introduction

[2] Recent studies have raised controversies about the predicted contribution of the Greenland Ice Sheet to global sea level change because of the poorly understood dynamic response of the marine-terminating outlet glaciers to climate forcing [Nick et al., 2009; Intergovernmental Panel on Climate Change (IPCC), 2007]. The ice loss of Greenland is dominated by both calving and meltwater runoff. Numerous observations and model results show a dramatic increase of ice flux into the ocean within a few years [Joughin et al., 2008a; van der Veen et al., 2011; Nick et al., 2009; Scambos et al., 2000]. Therefore, calving is a major component of the ice mass balance [Rignot & Kanagaratnam, 2006; van den Broeke et al., 2009]. However, it is one of the least understood processes in ice sheet dynamics with only sparse observational data. It consequently introduces large uncertainties in ice sheet models [Bassis, 2011; Bigg, 1999; van der Veen, 1999; Rignot et al., 2008]. Understanding the calving process and establishing a general calving law is still an unsolved problem in glaciology [Benn et al., 2007].

[3] The processes driving calving are rather complex and interdependent. In general, glacier flow is controlled by its stress regime, including both the internal and external forces acting at the boundaries [Meier and Post, 1987]. Since it is difficult to measure the forces controlling the behavior of the glacier directly, they are mostly determined indirectly by observations of the glacier's shape and its changes. For example, many of the major Greenland marine terminating glaciers show an acceleration in the last decade [Rignot and Kanagaratnam, 2006; Joughin et al., 2008a; Joughin et al., 2010; Moon et al., 2012], frontal thinning [Thomas et al., 2009; Abdalati et al., 2001], enhanced calving and massive retreat of the frontal positions [Podlech and Weidick, 2004; Moon and Joughin, 2008; Joughin et al., 2010]. Changed oceanic conditions in form of warmer ocean water leads to increased submarine melt rates, which may destabilize the frontal area of glaciers. This in turn could initiate thinning as well as frontal retreat and furthermore influence grounding line stability [Holland et al., 2008; Rignot et al., 2010; Motyka et al., 2011]. Additionally, increased melt water from enhanced summer surface melt may enter the glacier bed where it may decrease basal friction and thus causes higher flow velocities [Joughin et al., 2008a]. However, the latter process is only a minor effect on fast outlet glaciers [Joughin et al., 2008a]. Altogether, the interplay of these processes and its effects on the behavior of outlet glaciers remain poorly understood [Joughin et al., 2012].

[4] All these effects were observed at Jakobshavn Isbræ, one of the most prominent and fastest glaciers in Greenland. Jakobshavn Isbræ is located in a deep fjord trough with maximum depths of up to 1500 m and drains ~ 5.4% of Greenland's ice sheet area [Clarke and Echelmeyer, 1996; Motyka et al., 2011] with a recent ice discharge of 46 km³/yr into the Ilulissat Isfjord [Rignot and Kanagaratnam, 2006]. The front area of the glacier, which is relatively easy to access, has been well studied for over 150 years. The front retreated by 26 km between 1850 and 1950 (Figure 1) followed by a relatively stable phase until 2001 [Weidick et al., 1990; Podlech and Weidick, 2004]. Subsequently, a 16 km disintegration of the floating tongue of the glacier is visible in Landsat scenes acquired between 2002 and 2008. A small floating part was reestablished during the following winters. Since 2008, analysis of satellite images show a slow retreat of the frontal position with a large seasonal amplitude of about 5 kilometers [Amundson et al., 2008]. The advance and retreat of the frontal position correlate well with the change of ice mélange cover (a mixture of calved icebergs and sea ice) in the proglacial fjord [Sohn et al., 1998; Joughin et al., 2008b; Amundson et al., 2010]. Sohn et al. [1998] identified the gradually consolidated sea ice and icebergs in the Ilulissat Isfjord as the main reason for the advancing front during winter. In summer, the reduced force against the terminus that is caused by the weakened ice mélange in turn leads to high iceberg production rates and retreat [Sohn et al., 1998].

Figure 1

The Ilulissat Isfjord region: Landsat7 ETM + image of terminal region of Jakobshavn Isbræ from August 2002. White dotted lines indicate the approximate glacier front positions as described by [Weidick and Bennike, 2007], whereas the white solid line denotes the recent summer terminal position in 2010 (delineated from Landsat7 ETM + image). The filled green triangle shows the field camp position. The ocean tide prediction was done for a location near Ilulissat (red circle). The blue box shows the location of Figure 3. Inset shows location of Ilulissat Isfjord region in West Greenland.

[5] Simultaneously with the massive retreat of the frontal position of more than 15 km in the last decade, Jakobshavn Isbræ accelerated in summer from ~ 26 m/d in 2000 to 45 m/d in 2004 and thereby thinned at a rate of up to 15 m/yr Thomas [2009a], Joughin [2004a], Dietrich [2007a]. Besides thinning and acceleration, it is very likely that processes at the marine boundary play an important role for the current retreat [Holland et al., 2008; Joughin et al., 2012]. Holland et al. [2008] suggested that relatively warm ocean water which entered the Ilulissat Isfjord led to enhanced subsurface melt at the ice/ocean boundary and triggered recent changes at Jakobshavn Isbræ.

[6] The latter observations show the complexity arising from the interplay of how numerous processes affect a glacier's shape and dynamics. So far, no comprehensive theory has been developed to describe this complex system with its inherent physical properties and various controlling external forces. However, recent studies focus on the ice/ocean boundary and in particular investigate processes at the grounding line, the transition between grounded and floating glacier ice, which is believed to play a crucial role for ice sheet dynamics and is of particular interest for the stability of Jakobshavn Isbræ with its deep trough and inland sloping bed topography [Benn et al., 2007; Gladstone et al., 2010; Sole et al., 2008; Howat et al., 2007]. Model studies of Jakobshavn Isbræ propose that a grounding line at a reverse bedslope may cause an unstable retreat, which could continue some 80 km upstream [Vieli and Nick, 2011].

[7] There are a few methods which allow to precisely map the grounding line position. However, most of them are limited to slow moving ice shelf areas in Antarctica. The heavily crevassed grounding zones of many marine terminating outlet glaciers are not directly accessible and the usage of remote sensing techniques, such as Differential SAR interferometry (DInSAR) generally give good results, but require at least two SAR image pairs with a short temporal baseline [Rignot et al., 2011; Rignot, 1996; Hartl et al., 1994]. Other methods, e.g., analysis of altimetrically derived surface height profiles do not map area wide grounding line positions and have very sparse spatial distribution and resolution [Fricker and Padman, 2006].

[8] In this paper we propose a method for the detection of a continuous grounding line that is based on the analysis of 3D-motion fields obtained from terrestrial time-lapse imagery. Furthermore, the high temporal and spatial resolution of these motion fields allow for the analysis of the glacier flow and its variability during calving events. We demonstrate that this approach can contribute to a better understanding of the dynamic processes taking place at the calving front.

2 Methods

2.1 Field Setup and Observations

[9] In 2004, 2007, and 2010 we performed field campaigns close to the Jakobshavn Isbræ terminus in order to determine and analyze precise glacier flow patterns using monoscopic time-lapse photogrammetry.

[10] In August 2004 and 2007, a Kodak DCS 14n digital camera (focal length c = 50 mm) was deployed nearly perpendicular to the glacier's flow direction. An image sequence of roughly 1 day duration with a temporal sampling of 30 min was acquired [Maas et al., 2008]. A similar observation strategy was used in 2010, but with two redundant camera systems (Harbortronics Time-Lapse Package, Canon EOS 1000D, c = 35 mm). We obtained an image sequence of 29 days with a temporal resolution of 20 min. Figure 2 shows an example of one image from the sequence covering the calving front. In addition, the equipment deployed in 2010 is shown.

Figure 2

Color enhanced image acquisition of the glacier front of 19 May 2010. The yellow frame indicates the subregion used in Figures 4 and 5. The bottom right picture shows a modified Harbortronics Time-Lapse Camera Package with additional solar panel. The picture at the middle bottom position is a zoom of one installed fiducial marker.

[11] Due to the calving front retreat the camera position in 2010 was moved eastward and aligned to the recent glacier front (see Figure 3). Due to frontal retreat, the new camera field of view (FOV) does not overlap the 2004 observations and therefore does not allow for intercomparisons at identical positions. Table 1 gives an overview of analyzed image sequences used in this paper.

Figure 3

Camera field of view of image sequences in 2004 (red shaded area), 2007 (green shaded area), and 2010 (blue shaded area) draped over Landsat7 ETM + image of 7 July 2004. Prominent dark gray stripes are due to a Landsat7 sensor defect. Solid lines show glacier front positions in 2004 (red), 2007 (green), and 2010 (blue), respectively.

Table 1. Overview of Acquired and Analyzed Image Sequences Within This Paper

Sequence	Start	Duration	Sampling	Camera
Year	[month/d]	[days]	[min]
2004	08/20	~1	30	Kodak DCS 14n
2007	07/11	~ 6	30	Kodak DCS 14n
2010	05/07	~ 29	20	Canon EOS 1000D

[12] A crucial issue is the camera stability over time. We therefore installed fiducial targets as stable markers in the foreground of the camera FOV which can later be used to eliminate camera movements (see section 2.2.2). Additionally, a photogrammetric network was established to derive three-dimensional object coordinates of the glacier surface. For that purpose camera acquisitions from different positions and view angles were made and later processed in a stereo bundle adjustment. To ensure a stable reference frame GPS measurements were used to transform the local object coordinates of each epoch into the International Terrestrial Reference Frame (ITRF) [Dietrich et al., 2005].

2.2 Analysis of Image Sequences

2.2.1 Tracking of Surface Features

[13] To analyze the area-wide glacier flow, a thorough crevasse tracking scheme was applied. In contrast to the approach applied by Dietrich et al. [2007], which follows a distinct crevasse section through all images (Lagrangian specification), we used a stationary approach and analyzed the flow at an equidistant grid over the glacier surface with an adjacent node distance of 20 pixels in image space (Eulerian specification). This method has two advantages. First, the flow analysis is preserved at the stationary grid and does not vary in position with the moving crevasse pattern. Second, it avoids a position change of the observed distinct crevasse patterns with time and therefore does not introduce artificial movements into the tracking result. This fact is of particular importance for the analysis of long-time image sequences.

[14] Glacier movements between all subsequent images (t_i,t_i + 1) were calculated at each grid location using normalized cross correlation (NCC) in combination with a least squares matching (LSM) approach to enable subpixel accuracy [Gonzalez and Woods, 2008; Förstner, 1982]. LSM estimates up to six affine transformation parameters between two image patches and their precision. Scale changes and rotations between corresponding templates of consecutive images were not expected because of the high temporal resolution of the image sequences. Therefore, it was considered to be sufficient to solely calculate the two translation parameters in both image directions. The originally acquired raw images (RGB color space) were transformed into hue, saturation, intensity (HSI) color space and the matching was applied to the intensity channel. Prior to the matching the image templates were enhanced to obtain similar intensity and contrast. This avoids radiometrically induced correlation effects on the displacement components.

[15] Because of acquisition intervals shorter than 30 min and image sequence lengths of several days systematic effects in the displacement components occur that originate from the daily shadow movement at the glaciers surface. To compensate for these effects the LSM has been adapted in a way that pixels influenced by moving shadows are detected and excluded from the matching procedure. The iterative process starts with a matching using all pixels of the template as input values. The first result is the shadow-affected translation vector and the corresponding template of the second image which, at this stage, is an initial approximate solution. The difference image of the two corresponding templates gives information about possible shadow pixels. Applying a threshold value pixels with high difference values are separated and excluded in the next iteration step. The second matching should then result in an improved solution. This continues until the calculated translation vector does not change any more and thus indicates that the procedure converged.

[16] We chose a template size of 60 × 40 pixels which is a compromise between matching success and high spatial resolution. Due to the oblique viewing geometry we reduced the template height to 40 pixels in order to minimize the influence of distance-dependent scale variations within a patch.

[17] The feature-tracking results in a 2D motion field for each consecutive image pair (“optical flow”). A trajectory that documents the glacier motion at a fixed position in object space can be derived for each grid position.

2.2.2 Correction of Camera Movement

[18] The displacement fields derived from image tracking have to be corrected for the effects of camera motion caused by wind or temperature changes. Camera movements caused pixel displacements with maximum values of 2 pixels between subsequent images. Therefore, the trajectories had to be corrected for these small movements as well as the grid node positions to ensure crevasse tracking at stationary positions. For this purpose we observed the camera movement at stable foreground points (e.g., fiducial markers, well-identifiable natural features) as shown in Figure 2 and calculated the time-dependent translation and rotation parameters of the camera in a least squares adjustment. At each grid position and acquisition time the camera movements were consequently subtracted, providing stationary grid positions (further details in section 2.2.4).

2.2.3 Georeferencing of Image Measurements

[19] The final trajectories calculated for each grid position k have to be transformed into the object coordinate system taking into account distance-dependent scales and glacier movements nonperpendicular to the cameras viewing direction. Thus, the transformation procedure requires an approximate digital terrain model (DTM) of the glacier surface, camera orientation parameters and information about flow direction for each grid position.

[20] The DTM can be provided by additional data sets such as terrestrial laser scanner measurements (which we conducted during the campaign in 2007 [Schwalbe and Maas, 2009]) or multistation photogrammetric networks. Even though terrestrial laser scanner data can be recorded with high spatial resolution and point precision, we preferred to derive the DTM from images. A photogrammetric network allows for an integrated determination of 3D glacier surface points and the time-lapse cameras orientation parameters and thus provides a high inner accuracy. The determination of a precise camera orientation in relation to a laser scanner DTM would be a far more challenging issue. The image blocks were processed using the TU Dresden bundle adjustment software package [Schneider and Maas, 2007]. Necessary information for the georeferencing of the network were provided by GPS-measurements of the camera stations, natural height control points and control points obtained from theodolite measurements (see Dietrich et al., [2007] for further details).

[21] In case of a horizontally leveled camera setup with the camera viewing direction orthogonal to the glacier flow direction, trajectories could simply be scaled by the object-camera distance. Since these conditions can hardly be realized in practice, a more comprehensive method had to be applied. The image blocks were usually acquired at the beginning of the time-lapse measurements and include the first image of a sequence. The derived orientation parameters of the time-lapse camera allow for the reconstruction of an image ray for each pixel and its intersection with the DTM. Thus, each grid point (the first point of each trajectory) can be transformed into object space. With the assumption that each of these glacier points is moving within a vertical plane through its horizontal flow direction (azimuth), all 2D-points of a trajectory can be transformed into object space by intersecting their image rays with this model plane. The required horizontal moving direction for each grid point was obtained from vectorized flow lines in satellite images, but can also be inferred from multi laser scanner data sets [Schwalbe and Maas, 2009].

[22] From the transformed trajectories the vertical dz_k(t_i) (positive values indicate upward motion) and the horizontal (direction of flow, positive downstream) components at acquisition time t_i of the glacier flow can be derived with reference to a 3D position in object space. The displacement interval depends on the image acquisition frequency (e.g., 20 min). A more comprehensive description of the procedure for image sequence analysis which was implemented in C++ is given in Maas et al., [2008].

2.2.4 Error Budget

[23] Each glacier flow trajectory is affected by the errors resulting from the trajectory measurement in image space and by the trajectory georeferencing. Thereby the accuracy of the image space trajectories depends on the accuracy of the feature tracking and the uncertainty of the camera movement correction. The latter has the largest impact on the total measurement error. Together with a comparatively small-scale error, the total measurement error is about 0.15 pixels in image space. In general, the error in object space is proportional to the distance from the camera. For an object at a distance of 3000 m the measurement error amounts to 0.073 m (see Table 2). The absolute geolocation error of a trajectory is about 1–5 m.

Table 2. Error components Resulting From the Image Sequence Measurementa

Error Component	Image Space	Object Space
Camera movement correction	0.14 pixels	0.07 m
Feature tracking	0.1–0.3 pixels	0.05–0.15 m
Scale error	0.21 %	0.21 %
Total	0.18–0.35 pixels	0.09–0.17 m

• ^a Translated errors into object space refer to a distance of 3000 m.

[24] In the trajectories we furthermore observed an approximately diurnal signal with an amplitude of up to 0.2 pixels with a varying spatial pattern. We assume that these effects are induced by intensity changes caused by different sun illumination which affects the glacier tracking, non-uniform scale changes due to camera heating or refraction effects. This has to be considered in analyses that require a high temporal resolution of the trajectories.

[25] Independent flow velocities that were derived from repeated theodolite observations performed during the field campaign in May 2010 show a good agreement with flow velocities derived by photogrammetry with maximum differences of 4 m/d. Moreover, the residual differences between a flow velocity field derived from feature tracking in a Landsat7-ETM + image pair (2010-05-29 and 2010-05-20) and the averaged trajectory velocities during this period have a root mean square difference of about 2.8 m/d.

2.2.5 Determination of High-Resolution Flow Fields

[26] An adapted filter approach was applied to the trajectories in order to smooth the periodic diurnal fluctuations for a better interpretation. In order to preserve the exact start and end times of individual events (e.g., beginning of acceleration) the timing was manually determined from the unfiltered trajectories dv^Hz, dz and from the inspection of the image sequence movies (see Movie S1). During the break-up periods of each calving event a filter was applied with a short filter length of 6 h to preserve the rapidly changing flow velocities. Prior and after the calving events a robust local regression filter with a filter length of 1 day was utilized to attenuate the systematic diurnal residual errors mentioned in section 2.2.4. However, short-time velocity variations may be suppressed because of the long filter periods.

2.3 Determination of the Grounding Line

[27] The grounding line is defined as the point where the glacier ice loses contact with the subglacial bed and starts to float [Vaughan, 1994; Weertmann, 1974]. However, the grounding line is difficult to detect since it is a subglacial feature [Brunt et al., 2010]. The entire area between the grounded ice (limit of tidal flexing) and the free-floating ice shelf (hydrostatic point) is often called grounding zone with a typical width of several kilometers [Vaughan, 1994; Smith, 1991; Rignot et al., 2011]. Because of the tidally induced vertical movement of the ice, the grounding line moves back and forth during a tidal cycle with a varying width mainly depending on the tidal amplitude and the slope of the subglacial bed [Rignot et al., 2011; Echelmeyer et al., 1991]. Consequently, throughout the paper we use the term grounding line where the tidally induced vertical movement of the glacier can be first distinguished from the measurement noise of the 3D trajectories. It is approximately the position of the true grounding line and close to the upper limit of tidal flexing.

[28] In general, there is little information about the grounding line locations and their migration with time for most fast moving outlet glaciers. Echelmeyer et al. [1991] inferred grounding zone positions at Jakobshavn Isbræ indirectly from a longitudinal surface height profile and satellite imagery, but the use of optical imagery is uncertain to 500–5000 m and limited to the detection of the inflexion point [Vaughan, 1994]. It is not clear from previously published results where the grounding line location of Jakobshavn Isbræ was and recently is [Motyka et al., 2011]. For example, published grounding line positions differ substantially between 1–2 km [Motyka et al., 2011; Thomas et al., 2003; Csatho et al., 2008]. The differences can be attributed to the different data and its varying acquisition times (where the position of the grounding line may have changed) as well as to the different analysis methods.

[29] In the following we present a method which allows for an area-wide mapping of the grounding line without accessing the glacier surface.

2.3.1 Ocean Tides

[30] For the determination of the grounding line, information about the tidal signal is required. We synthesize a time series of the tidal elevation h(t) in Disko Bugt using the TPXO.6.2 ocean tide model [Egbert and Erofeeva, 2002] with the main tidal constituents (M₂, K₁, S₂, O₁, N₂, P₁) at the sampling rate of the image acquisition. Since the TPXO.6.2 ocean tide model does not allow for the calculation inside the fjord, we correlated the synthesized signal with the vertical motion of fjord ice and estimated a phase shift of ∼ 4 min that was consequently applied to all trajectories. The correction is needed for the relative temporal adjustment of the trajectories to the synthesized tidal signal, however, it is small compared to the image acquisition frequency of 20–30 min. The phase shift can be attributed to the time it takes the tidal wave to transit the distance from Disko Bugt to the glacier front (ca. 50 km) and to uncertainties of the tidal constituents (in particular the phases) of the ocean tide model TPXO.6.2 [Richter et al., 2011]. The height variations of both signals are in a good agreement and no amplitude scaling of the trajectories was applied. This is consistent with tide gauge measurements in Ilulissat and tide pole readings close to the glacier front during the field expedition in 2004 [Dietrich et al., 2007]. The tidal range in front of the glacier terminus is about 2.5 m and therefore easily detectable by means of photogrammetric time-lapse imagery analysis.

2.3.2 Tidal Influence on Vertical Ice Movement

[31] The component dz_k(t_i) of each trajectory was corrected for slope and is the vertical displacement perpendicular to flow direction between the acquisition times t_i and t_i + 1. Small residual across-flow displacements that were not fully corrected during the image sequence analysis may superimpose the vertical signal, but can be neglected here (see section 2.2). According to this, the change of tidal elevation dh = h(t + 1) − h(t) between subsequent image acquisitions is used for further investigations. Some dz values contain spurious displacements originating from the image matching process. In order to remove these spurious displacements we smoothed dz using a robust local regression filter (Matlab filter ’rlowess’) with a filter length of 100 minutes. However, a few spurious displacements remain after robust filtering. Thus, integrating dz would introduce steps and spikes into the absolute displacement z(t) and makes it difficult for further usage. We therefore used dz and accepted a higher noise level. Figure 4 shows how well both signals correlate using the example of a point at the ice mélange in the Ilulissat Isfjord.

Figure 4

(top) Color enhanced image of 30 May 2010 with the newly established glacier front (red line) after a big calving event and an analyzed trajectory position (filled green star). (bottom) Observed vertical image-to-image displacement dy (light blue curve) and robust filtered and smoothed curve (black) as well as corresponding ocean tidal signal between subsequent acquisitions dh calculated from ocean tide model TPXO.6.2 (green curve). The figure shows a good agreement in both amplitude and phase between modeled tidal signal and observed vertical displacement.

[32] To distinguish whether the vertical movement of the glacier is driven by ocean tides, a cross correlation approach with normalized signal amplitudes and a correlation length of N time-series of camera acquisitions was performed between the tidal signal dh(t) and the vertical component dz(t) of a trajectory k. and denote the averaged values of dh, dz:

(1)

ρ_k = ρ_k(Δt) yields the cross correlation coefficient of both signals shifted by Δt in time against each other. Accordingly, the maximum correlation coefficient ρ_k^max at Δt_k^max was found by

(2)

[33] Applying equations (1) and (2) to all trajectories yields maps of ρ^max and corresponding Δt^max. The calculated delay Δt^max of the observed vertical movement of thetrajectories in comparison with the tidal signal (Δt_k^max) is constantly 60–80 min. A spatial pattern of the time delay, however, could not be found.

[34] The freefloat F is the ratio between the signal amplitudes z(t) and h(t) or dz(t) and dh(t), respectively. F is derived by minimizing ||dh(t) − F ⋅ dz(t − Δt_k^max)||² in a least squares sense. Δt_k^max was applied to co-register both signals and was derived by equation 1. A value of F = 1.0 indicates full hydrostatic equilibrium of a certain object point, while lower values are damped by the ice body or are partly grounded. Figure 5 shows a map of percentage freefloat values for a 117 hour sequence starting on 14 May 2010, 7 days before the main calving event occurred.

Figure 5

Map of freefloat values of image sequence analysis. Delineated grounding line is shown as white line over a thick black line for better visibility. The underlying color enhanced digital image was acquired on 19 May 2010 and shows the subregion as indicated in Figure 2. The approximate position of the glacier front is shown as yellow line.

2.3.3 Delineation of the Grounding Line

[35] The location of the grounding line is derived from the freefloat values shown in Figure 5. High values of ρ denote a good coincidence of the vertical ice movement with tides, while values below 0.4 indicate less or no tidal influence. There is a region of high correlation in the frontal area diminishing abruptly ∼ 550 m upstream from the front. This area was manually extracted (white line in Figure 5) and indicates the grounding line position. The accuracy of the manual mapping of the grounding line is within 100 m and depends mainly on how well the area of high freefloat values at the front can be delineated from the background noise.

[36] A further error source is the grounding line migration during a tidal cycle which mainly depends on both tidal range and bedrock slope [Echelmeyer et al., 1991]. Smith [1991] stated grounding line migration values up to 130 m in ice shelf areas of Antarctica. We could not detect any grounding line migration within the tidal cycle. A possible migration is probably below the detectable mapping accuracy. The limiting factor for grounding line migration could be a relatively steep bedrock slope beneath Jakobshavn Isbræ's grounding line.

3 Results

3.1 Grounding Line Migration Between 2004 and 2010

[37] We applied the described method to the acquired image sequences of 2004, 2007, and 2010 and transformed the delineated grounding line positions from the image space system into the object space (see 2.2.3). Figure 6 shows the freefloat values (color-coded dots) and the inferred grounding line positions (red lines) of the field campaigns. We could not detect any tidal signal in the observations made in summer 2007 and approximated the grounding line position to be identical with the glacier front.

Figure 6

Freefloat values (color-coded dots) in object space with derived grounding line positions (red lines) from image sequences of August 2004 and May 2010 plotted over Landsat7 ETM + image of 7 July 2004. Dotted red line indicates the approximated grounding line in July 2007. The black line shows an ice flow trajectory at the center of the main trunk. The blue box denotes the area shown in Figure 9.

[38] Reanalyzed freefloat values for the image sequence of 2004 [Dietrich et al., 2007] show an approximately 500 m wide floating portion along the glacier front (see Figure 6). Dietrich et al. [2007] detected the full tidal signal in the frontal proximity with decreasing freefloat values upstream. In contrast to the summer observations of 2007 and 2010 a floating tongue still existed in late summer of 2004.

[39] In 2009/2010 the advanced winter front was only a little west of the summer front of 2009 and the front was already well grounded when the field equipment was installed on 7 May 2010. In the following weeks the front advanced and a small floating part was reestablished again. During the readvance the grounding line location was monitored using daily image sequences. First indications of a small free-floating part were observed on 10 May 2010. The floating part increased to 2.5 km along the glacier front and reached ∼ 500 m inland until it broke up on 20 May 2010 at about 20:00 local time (equivalent to UTC-2 h). During the readvance the grounding line remained stable at the position shown in Figure 6.

[40] During the summer months the position of the grounding line coincides approximately with the glacier front. However, a small floating part (usually smaller than 500 m) can be established during the readvance of the glacier front and breaks apart after subsequent calving events. Thus, the glacier front is floating during the winter and ephemeral during the summer.

[41] Between 2004 and 2010 we determined a grounding line retreat of 3.5 ± 0.2 km along the center line of the ice flow (the center line was inferred from flow velocity gradients derived by feature tracking from a Landsat7 image pair of 1999-09-11 and 1999-08-28). The observed retreat corresponds to a retreat rate of approximately 600 m/yr, which agrees well with average rate of retreat (0.6 km/yr) of the late summer calving front position from 2006 to 2009 [Joughin et al., 2012]. The inspection of Landsat imagery revealed that the frontal positions during the field campaigns were nearly the locations of the maximum calving front retreat of the corresponding year.

[42] A comparison with bedrock topography data from Plummer and van der Veen [2008] shows that the ice at the center line grounding line position rested at -710 m in 2004 and was located at -1050 m in 2010 (see Figure 7). Therefore, the grounding line position retreated to a 370 m deeper position. If the depth is over 1000 m, the calving face would have to be higher than 100 m to be grounded. We found values of the calving face of up to 135 m using long range terrestrial laser scanner measurements in July 2007 [Schwalbe and Maas, 2009]. However, the bedrock topography was derived from a compilation of profiles derived from airborne ice/snow penetrating radar flights conducted between 1997 and 2006 and can show bedrock features which are influenced by interpolation effects.

Figure 7

(top) Color-coded bedrock topography of the glaciers frontal region (CReSIS data from Plummer and van der Veen [2008]) with the prominent and more than 1300 m deep channel of the Jakobshavn Isbræ's main trunk. Grounding line positions of 2004, 2007, and 2010 are shown as red lines. The black line denotes the center flow line, the dashed purple line indicates the approximate grounding zone position for summer 1985 derived by Motyka et al. [2011]. (bottom) Bedrock profile (black line) along the center line with grounding line positions (dashed vertical lines). From 2004 to 2010 the grounding line migrated about 3.5 km to the east and the recent grounding line position dropped by 370 m.

3.2 Observation of Flow Velocity Changes During a Major Calving Event

[43] The analyzed calving event occurred on 27 May 2010 at about 9:00, when an approximately 3.0 × 0.6 km large area of the glacier front calved into the Ilulissat Isfjord (see Movie S1 of the supplemented online material). The sequence used is a 9 day long subsection of the acquired image sequence starting on 24 May 2010 (see Table 1). We analyzed the temporal change of both the surface parallel flow velocity (see Figure 8 and 9) and the vertical velocity variations (see Figure 10). Both figures exemplarily show the flow velocity changes for three locations along the center line of the glacier. Additionally, Movies S2 and S3 show the temporal evolution of flow velocity changes in the frontal glacier area for the horizontal and vertical component, respectively. Figure 8a visualizes the spatial distribution of the maximum flow velocities and indicates the break-up zone (area between yellow and red curve). During the break-up phase, we inferred peak velocities of up to 70 m/d close to the new glacier front (red curve). Observations made by Amundson et al. [2010] in 2008 obtained values in the order of 60 m/d prior to the calving event for individual positions.

Figure 8

(a) Maximum flow velocities during the calving event plotted on a digital image after the major calving event on 27 May 2010. The red line shows the glacier front after the calving event, the yellow line indicates the front prior the calving event. Positions and numbers in circles refer to Figures 8b, 8c, and Figure 10. (b) Horizontal displacement of trajectories at three different positions. The trend prior to the calving event on 27 May 2010 was removed from all trajectories. (c) Velocity change during calving event at individual positions. Thick red vertical lines denote the main calving event, thin lines indicate small calving events without significant changes at the glacier front. All curves show an abrupt increase of flow velocity with slowly decreasing speed over several days after the occurrence of a calving event.

Figure 9

Color-coded percentage of short-time velocity change plotted on Landsat7 ETM + image of the glacier front on 29 May 2010. The percentage values were derived from the maximum velocity during calving event versus the velocity prior to the calving event. The yellow circle denotes the camera position of the image sequence. The yellow line shows the front position prior to the calving event.

Figure 10

(a) Maximum vertical velocities during the calving event plotted on a digital image acquired prior a major calving event on 27 May 2010. The red line shows the glacier front after the calving event, yellow line indicates the front prior the calving event. Positions and numbers in circles refer to Figures 10b and 10c, respectively. (b) Vertical displacements during the calving event at marked positions. (c) Vertical velocity variations at marked positions. The green curves show the filtered signals, black curves represent the unfiltered measurements. Calving events are denoted as red vertical lines. After break up of the glacier front, no data was available at positions 1 and 2.

[44] In the following, temporal flow changes at positions 3–5 (Figure 8) located approximately along the center flowline and beyond the postcalving front are discussed in detail. The horizontal flow velocity only started to accelerate at the onset of break up. Position 3 accelerated from 29 m/d to 59 m/d (103 %) during only 12 hours. In the same time positions 4 and 5 accelerated by 53 % and 32 %, respectively. The velocity increase happened in a step-like fashion, very similar to the velocity changes during a calving event observed by Amundson et al. [2008] at Jakobshavn Isbræ or at Helheim Glacier [de Juan et al., 2010]. The spatial pattern of acceleration is shown in Figure 9. Flow velocity changes of more than 100 % during the calving event compared to the precalving velocity were observed at positions up to 300 m upstream the calving front. With increasing distance from both the terminus and the center flow line, the relative change in flow velocities decreases. The upstream limit of velocity changes could not be identified clearly, because the accuracy of the flow velocities in slow flowing areas is not precise enough. The detection threshold of flow change is about 30 %. Despite this, flow changes caused by calving could be identified at least up to 1 km upstream. The rapid acceleration is followed by a slow decrease of flow velocities over a period of 4–5 days, but remained above the precalving velocity.

[45] In agreement with results of Amundson et al. [2010], the horizontal flow velocities show no significant variation prior to the calving event. On the other hand, the vertical component shows large displacements a few days before. Figure 10 illustrates the uplifting and lowering of the glacier front prior and during the calving event. On 25 May 2010 (4:40) ∼ 33 hours before the main calving event occurred, a 20 m wide ice band, extended 500 m along the glacier front, capsized in the northern part of the main trunk and triggered an uplifting of the glacier front (Position 1 in Figure 10c). The lowering beyond the postcalving front is shown in Figure 10c, Position 3. During this period, position 1 was lifted about 15 m, while position 3 dropped by 8 m. The lowering of the glacier surface could be identified at positions 500 m upstream the calving front, but with decreasing amplitude for increasing distance from the new glacier front. The lifting at the glacier front together with the observed lowering upstream indicates a bottom out rotation of the iceberg, although the 20 minute image sampling does not allow a direct verification of that. After the break up of the frontal area on 27 May 2010, the new front lowered rapidly by 20 m (Position 3, Figure 10c). The vertical velocity adjusts to the precalving values over the next 4–5 days which is similar to the slow-down time of the horizontal flow velocity.

[46] A comparison of both the horizontal flow velocity (see Movie S2) as well as the lifting and lowering (see Movie S3) of each glacier point in the lower reaches highlights the similarity in spatial pattern and temporal decay after the break up.

[47] Prior to the calving event on 27 May 2010 two slightly smaller calving events were identified. The first started on 20 May 2010 (20:00) with an area loss of 2.5 × 0.3 km. Subsequently, a 3.0 × 0.25 km part of the glacier front broke up. Together, both calving events calved a nearly equal area compared to the calving event on 27 May, but with different positions of the calving face after the calving. The analysis of this event showed a similar behavior of the vertical and horizontal flow velocity evolution, but it was restricted to a 200 m wide area of the southern part of the glacier front with slightly lower postcalving peak velocities not exceeding 50 m/d and a shorter decay time of 2 days.

[48] In addition to the temporal variations, a trend analysis of the 3D trajectories gives an estimate of the dip angle of the trajectories (see Figure 11). The dip angle is approximately the gradient of the surface slope which in turn can define the limit of the break-off edge. The steep dip angles upstream the red line in Figure 11 indicate rapidly rising surface heights and, thus, disclose that ice thickness exceeds the limit to where calving is possible. Additionally, in agreement with Dietrich et al. [2007] we observed the highest flow velocities in areas of steep dip angles. For more details on calving theory we refer to Amundson et al. [2010].

Figure 11

Area-wide dip angles of the 3D trajectories (negative values indicate downward pointing flow trajectories). The yellow and red lines delineate new glacier fronts after two individual major calving events. The calving zone (left to the red line) is characterized by an almost horizontal surface. Beyond the red line, a prominent slope change with values up to -6 degrees is clearly visible.

[49] No correlation of both horizontal and vertical flow velocity components with the tidal signal was found, indicating that the glacier front is well grounded in this area (further discussed in section 4.1).

4 Discussion

4.1 Tidal Modulation on Horizontal Flow Velocity

[50] Short-time horizontal velocity changes can be linked to ocean tides. Observations at ice shelves and ice streams in Antarctica indicate that relatively minor tidal fluctuations can cause large velocity changes of up to ± 50 % at the lower glacier region, but a weak signal could also be detected 85 km upstream [Bindschadler et al., 2003; Gudmundsson, 2011; Anandakrishnan et al., 2003]. In Greenland, studies at Kangerdlugssuaq Glacier show horizontal displacement variations of 0.5 m [Davis et al., 2007] (10 % change of flow velocity) during a tidal cycle. Detailed investigations by de Juan et al. [2010] at Helheim Glacier revealed tidal modulation of flow velocity after a calving event at positions at least 12 km upstream of the glacier front with no significant vertical variations with tidal frequencies, indicating that the glacier front is well grounded. Most observations show that velocities decrease during rising tide and accelerate during lowering [Anandakrishnan and Alley, 1997; Bindschadler et al., 2003]. Moreover, most studies found horizontal flow variations induced by tides regardless of whether a vertical motion was detected or not (e.g., de Juan et al., [2010]). Thus, this indicates that change of back force modulated by tides can have a large influence even if the glacier is well grounded [Walters, 1989].

[51] At Jakobshavn Isbræ, results of field measurements between 1984 and 1986 by Echelmeyer et al. [1991] showed velocity variations during a tidal cycle of 35 % of the former existing large floating tongue. In contrast, after the nearly complete disintegration of the floating tongue no significant horizontal modulation by tides was found since 2004 [Dietrich et al., 2007; Amundson et al., 2008]. However, observations of the ice mélange by [Amundson et al., 2010] show a 4 % modulation of the horizontal displacement with the tides, but with no notable effect on the flow velocity of the glacier.

[52] All our field campaigns were placed close to spring tide to increase the potential effect of tides on the flow dynamics. After applying equation (1) and (2) to the horizontal component dv^Hz of the analyzed trajectories we found no significant correlation (ρ < 0.5) with the tidal signal at any point of the observed glacier area during the field campaigns in 2004, 2007, and 2010. During the observation time, the glacier was well grounded or had a short floating tongue of less than 1 km. Despite the lack of tidally modulated ice flow, the glacier exhibits significant vertical motion with tides.

[53] Horizontal flow changes in the order as observed at Helheim, Kangerdlugssuaq and other major outlet glaciers should be well detectable by the applied observation method. We conclude that the horizontal flow changes due to tides—if there even are any—were below the detection accuracy of ± 5 % of the flow velocity (at the center of the glacier front) and thus indicates that the influence of tidal modulation on horizontal flow variations at Jakobshavn Isbræ is small.

4.2 Calving Induced Flow Velocity Changes at the Glacier Front

[54] Our observations of the fast lifting of the glacier front prior to a calving event indicate that the frontal area is breaking away from glacier. The area of lifting approximately delineates the region of the new iceberg and is already visible 2 days prior to the break up. The lifting pattern suggests that the calving occurred bottom out. Additionally, the second analyzed calving event most likely also calved bottom out. Both events were located near the grounding line where the glacier front is close to floatation. These observations agree well with the model calculations made by Amundson et al. [2010].

[55] The horizontal velocity variations started with the break up and were restricted to a small area at the glacier terminus. In general, the velocity decreases during advance and increases during the retreat of the glacier front. The latter agrees well with the findings by Joughin et al. [2012]. Moreover, the large velocity changes led to increased longitudinal strain rates. The start of the short-time velocity variations coincide with the break up of the glacier front and seem to be linked directly to calving front changes and thus showed a similar behavior to observations by Nettles et al. [2008] at Helheim Glacier. Nettles et al. [2008] suggested that the velocity increase is most likely due to the decreased resistive extensional stress against the glacier face [Howat et al., 2005]. This can be suggested at Jakobshavn Isbræ, too. However, the velocity changes could also be triggered by an increased meltwater input which in turn could decrease the basal effective pressure and could accelerate the flow velocity. But it is unlikely that the doubling of the velocity change is initiated by meltwater, because studies show that enhanced meltwater input on fast flowing outlet glaciers has a minor effect on the flow velocity changes [Echelmeyer and Harrison, 1990; Andersen et al., 2011; de Juan et al., 2010]. Moreover, the velocity acceleration would in this case not only be restricted to the small area at the glacier front. Studies by [Iken et al., 1993; Lüthi et al., 2002] suggest that a thick layer of temperate at the base could explain the fast flow velocities.

[56] The observations of this section show further that individual calving events are interlinked and may trigger each other. Moreover, the induced stress changes caused by a calving event affects the stability of the lower glacier areas in a way that the readjustment to a new stationary geometry can last several days. Because of a limited spatial coverage, we could not investigate possible implications on the glacier ice dynamics further upstream. Nevertheless, these large variations of flow velocity changes solely caused by calving processes were observed during short time periods of a few hours. This variation has a minor effect on satellite-based flow velocity estimations which are usually based on a temporal separation of more than a day.

[57] We used satellite images to investigate a potential link between the change of ice mélange cover of the Ilulissat Isfjord and the onset of major calving events. From MODIS and Landsat imagery a sharp border between the dense ice mélange and the ice free surface with sparsely distributed icebergs was identified 20 km west of the glacier front on 14 May 2010. During the next 6 days the border of dense mélange progressively retreated to the east until the calving event occurred. Because of the extensive cloud coverage in the area the maximum retreat of the dense mélange could not be determined, but retreated to at least 10 km toward the front of the glacier, resulting in a retreat velocity of 1.6 km/d. In agreement with Amundson et al. [2010], after the calving event the entire fjord becomes rapidly covered with ice mélange without any large ice free areas. The retreat concomitant starts with increasing spring tide and may also have an effect on the timing of calving events. However, the causes and mechanism of this retreat cannot solely be determined by satellite observations, because they have a very sparse temporal and spatial resolution.

5 Conclusion

[58] Based on the analysis of time-lapse imagery of the glacier front, we developed a method to precisely map the grounding line and applied this approach to field data obtained in 2004, 2007, and 2010. At Jakobshavn Isbræ, we found a grounding line retreat of 3.5 km between 2004–2010. Including the results of Motyka et al. [2011], the grounding line retreat between 1985–2010 is about 6 km. These findings may help to improve dynamic glacier models since they lack reliable data on grounding line retreat [Gladstone et al., 2010]. The observations show further that the grounding line usually coincides with the glacier front in summer time. However, a small ephemeral floating tongue can be generated during the readvance of the glacier after calving events and is not only established during winter.

[59] Moreover, the image sequences were processed in order to infer flow velocities of the lower glacier reaches with high temporal and spatial resolution. We focused on the analysis of flow velocity changes during a major calving event. Horizontal flow velocities accelerate immediately with the onset of the frontal break up and can reach velocities of up to 70 m/d, some locations even accelerate by 140 %. After the calving event, the glacier readjusts to the new stationary geometry with slowly decreasing flow velocities within a period of 4–5 days. In addition, large vertical lifting at the glacier front in the order of 15 m and lowering of about 8 m at positions 500 m beyond the front occur prior to the calving event and may trigger the onset of the break up. The observed calving causes large temporal and spatial changes in the stress and flow regime of the lower glacier reaches. Depending on the size of the calving event, effects on flow velocity were observed at least up to 1 km upstream with respect to the new glacier front. Finally, the results could be incorporated in glacier and ice sheet models to parameterize calving. The presented observation method and analysis technique may help to adapt similar approaches at other glaciers to study short-period variations in glacier flow.

Acknowledgments

[60] The research was funded by the German Research Foundation (DFG) under grants DI 473/30-1 and MA 2504/5-1. We thank Air Greenland, Jens Ploug Larsen, and Uli Ungethüm for the logistic support. The research permit was provided by the Greenland Home Rule government. Comments from M. Truffer, M. P. Lüthi, J. Amundson and an anonymous reviewer improved the manuscript substantially.