An Intensive Observation of Calving at Helheim Glacier, East Greenland

16 17 Calving of glacial ice into the ocean from the Greenland Ice Sheet is an important 18 component of global sea-level rise. The calving process itself is relatively poorly 19 observed, understood, and modeled; as such, it represents a bottleneck in improving 20 future global sea-level estimates in climate models. We organized a pilot project to 21 observe the calving process at Helheim Glacier in east Greenland in an effort to better 22 understand it. During an intensive one-week survey, we deployed a suite of 23 instrumentation, including a terrestrial radar interferometer, global positioning system 24 (GPS) receivers, seismometers, tsunameters, and an automated weather station. We 25 were fortunate to capture a calving process and to measure various glaciological, 26 oceanographic, and atmospheric parameters before, during, and after the event. One 27 outcome of our observations is evidence that the calving process actually consists of a 28 number of discrete events, spread out over time, in this instance over at least two days. 29 This time span has implications for models of the process. Realistic projections of future 30 global sea level will depend on an accurate parametrization of calving, and we argue that 31 more sustained observations will be required to reach this objective. 32 33 34

We sought to answer the following questions: 82 83 • Based on scientific and logistical considerations, we chose Helheim Glacier in east 92 Greenland as our study site (Fig. 1). The observations we report and the conclusions we 93 draw represent a pilot effort, essentially demonstrating the utility of combining certain 94 glaciological, oceanographic, and meteorological observations relevant to the calving 95 process. Most importantly, our pilot effort demonstrates the potential for a deeper 96 understanding of calving to be achieved through future similar, sustained in-situ 97 observations. 98 99 The outline of this paper is as follows. The next section reviews existing calving theories 100 and parameterizations and how they motivate our field work. The field work section 101 describes our instrumentation and presents our key observations. The final section 102 summarizes our findings and points to future field and modeling activities related to 103 calving. 104 105

EXISTING CALVING PARAMETERIZATIONS 107 108
The overarching goal of our work is to develop a viable parametrization of calving that 109 can be used in global climate models to better project sea-level change arising from 110 Greenland mass loss. A simple, universal calving law might be illusory, and many 111 different calving mechanisms likely exist [Van der Veen, 2002; Benn et al., 2007;Vieli & 112 Nick, 2011]. To aid the reader in understanding the current state-of-the-art in calving 113 models, we provide some background on current theory, and how various existing 114 parameterizations bear on the types of observations we undertake. Of course, not all 115 physical variables are easily observable, particularly those at depth in the glacier, and 116 this limits to some degree our field observation possibilities. A number of mechanisms 117 have been discussed in the literature as triggers for glacier front calving (Fig. 2), and are 118 presented below. Calving may be dominated by any one of these mechanisms, or a 119 combination, or by mechanisms yet not envisaged. 120 121 The interaction of calving with the motion of the glacier itself is intricate, and raises the 122 question: does calving cause change in the glacier flow field, vice-versa, or both? Some 123 researchers point out that calving leads to a reduction in the backstress and therefore an 124 acceleration of the glacier, considered over many calving events [ simulations of Helheim Glacier [Nick et al., 2009] and a force balance analysis [Howat et 129 al., 2005] suggest that the recently-observed glacier acceleration, thinning, and retreat 130 originate at the calving terminus and then propagate upstream due to changes in 131 geometry and driving stress. These findings motivate us to observe motions at the 132 calving front, and to ascertain if changes further upstream occur before or after calving.

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Calving and associated glacial earthquakes have been previously observed at Helheim 135 Glacier [Nettles et al., 2008] During a one-week period in August 2014 we deployed a suite of in-situ instrumentation 252 (Fig. 3) to observe glacier behavior before, during, and after a calving event. Our 253 instrumentation included: an on-land terrestrial radar interferometer (TRI), on-land 254 broadband seismometers, an automated weather station (AWS); on-ice GPS receivers, 255 on-ice seismometers; and an in-ocean tsunameter array. We were fortunate in that a 256 major calving event occurred during our one-week observational period.

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The TRI mapped the evolution of the displacement field of the glacier surface and its 259 elevation both upstream of the front and downstream over the mélange, at two-minute 260 intervals. These measurements were sustained over the entire week. The on-ice GPS 261 instruments recorded three-dimensional motion of the glacier along a flow band. We 262 simultaneously observed seismic activity in the glacier from a set of broadband 263 seismometers that were collocated on the glacier with the GPS, as well as two additional 264 broadband seismometers located on the land adjacent to the calving front. Ocean wave 265 disturbances in the adjacent fjord were monitored from a nearby tsunameter array. 266 Finally, we visually recorded calving events using a time-lapse camera at the nearby 267 AWS, which recorded temperature, humidity, solar and infrared radiation, and wind.
The centerpiece of our field instrumentation is a TRI. The commercial TRI instrument that we used is an interferometric, Ku-band (1.74 cm 296 wavelength), real-aperture radar that provides high-resolution intensity and phase images 297 [GAMMA, 2016]. Operating at 17.2 GHz, instrument displacement sensitivity is better 298 than 1 mm [Werner et al., 2008]. The instrument has a nominal range resolution of 0.75 299 m, and an azimuth resolution of 7.5 m at a distance of 1 km, which decreases linearly 300 with distance. The radar has one transmitting antenna and two receiving antennas, 301 typically separated by 25 cm baseline, positioned on a rotating frame (Fig. 4a) To provide the reader with a sense of the kind of data product that TRI can produce, see 319 Fig. S1 in Supp. which shows a typical velocity field for Helheim from our TRI data using 320 feature tracking and overlaying a coincident elevation field. The flow of the glacier in this 321 instance is clearly plug-like, with shearing isolated to relatively thin basal and lateral 322 boundary layers, so that the most important strain rate is longitudinal. In future 323 deployments, we hope to deploy two radars in order to acquire rapid interferometric 324 updates to the velocity field, in stereo. This is useful, as a single radar can only provide 325 one TRI scan area before, during, and after the primary calving event (Fig. 5) reveals some of 340 the complexity of the calving process. The initial glacier front peeled back in a multi-step 341 process. From radar intensity images, we can evaluate the position of the calving front 342 and observe its multi-step retreat (Fig. S3 in Supp.).

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A useful metric for surface change can be derived from interferometric correlation, which 345 measures the similarity of scattering characteristics between consecutive radar images (a 346 high correlation implies that the surface is not changing). This metric is typically used to 347 judge phase quality for interferometric phase unwrapping. Here, we use maps of 348 interferometric correlation coefficients between successive two-minute images to 349 determine periods of rapid surface change related to calving. Although the primary 350 event took place at 06:37 UTC on August 12, we observed a strong drop in correlation 351 around 05:46 UTC (approximately an hour before the primary calving event) along a 352 linear, crack-like, surface expression about 400 m upstream of the terminus (Fig. 5, red  353 dots, and Fig. S4 in We evaluated the strain rate field over the northern trunk of the glacier by spatial 360 differencing (in the horizontal direction) TRI velocity maps, adjusted to match the 361 approximate direction of flow (Fig. S5  GPS devices measure ground motion in three dimensions, at higher frequency (period < 384 1 min) and in greater precision (centimeter-level) than TRI. Moreover, TRI usually only 385 provides a single component of motion (the projection of the true velocity vector onto the 386 look vector of the TRI), whereas GPS data determine displacement in three dimensions.

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A shortcoming, however, is that GPS receivers can in general only be deployed at a 388 handful of locations, and thus yield spatially-sparse observations, while TRI provides 389 effectively millions of measurements every few minutes. 390 391 To monitor higher-frequency (period <1 min) glacier motion, we installed six GPS stations 392 (Fig. 4c) along a central flowline on the northern trunk of the glacier. All GPS sites were 393 deployed early on August 9, 2014 and retrieved later on August 15, 2014. One GPS site 394 ceased recording a few hours after deployment due to an internal fault and a second site 395 failed on the morning of August 11, 2014, after the anchor system melted out of the ice. 396 Each site consisted of dual-frequency receiver (Trimble NetRS 5700 with Trimble Zephyr 397 Geodetic antennas), which collected moderate-rate (1 Hz) GPS data. Positions were 398 determined using differential carrier phase positioning [Chen, 1998] relative to a 399 permanent, fixed GPS receiver at the nearby town of Kulusuk (~100 km away). 400 Horizontal and vertical uncertainties are approximately 5 and 10 cm, respectively. 401 Geodetic solutions were transformed to a northern hemisphere polar stereographic 402 projection centered on Greenland  Seismometers can provide ground velocity in three components, by measuring 443 accelerations. We used broadband instruments, which cover a wide range of frequencies 444 (well below 1 Hz), allowing observation of glacier and land velocity at a much higher rate 445 than our GPS or TRI instruments. The benefit of installing seismometers on the glacier is 446 that they are sensitive to icequake (high frequency cracking of the glacier) and sudden 447 slip events (short duration increases well above background speeds). The advantage of 448 installing on nearby land is that the stations can be utilized for a much longer period of 449 time (several years). We established on-land sites on a rolling basis over the last several ( Fig. 4c) co-located with the GPS array mentioned above, and also on land (Nanometrics 456 Trillium 120), on opposite sides of the calving front (Fig. 4d).

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When a calving event happens, the seismic waves that emanate from the glacial fracture 459 take different amounts of time to reach each seismic station, depending on the distance 460 from the fracture to the station. It is then a straightforward calculation to invert for location 461 given a standard velocity of seismic waves through ice and travel time to each station. 462 Surprisingly, we found that the calving energy propagated at a much slower speed 463 (~1,600 m/s) than the typical compressional wave speed in ice (3,800 m/s). We 464 developed a method of determining glacier calving locations using seismic wave arrival 465 times from paired local seismic stations [Mei et al., 2016]. In short, the difference in 466 surface wave arrival times for each pair of stations is used to define a locus (hyperbola) 467 of possible origins. With multiple pairs, this can be used to triangulate the origin of the 468 seismic waves, interpreted as the calving location. Our different approach was motivated 469 by difficulties with traditional seismic location methods that fail due to the emergent 470 nature of calving, which obscures the primary and secondary wave onsets, and the close 471 proximity of the seismometers, which combines body and surface waves into one arrival. 472 As a summary of that previous work, our locations determined from seismic data match 473 the location of calving determined by time-lapse cameras and remote sensing. 474 475 On August 12, while camped near the calving front our team was awoken by a sustained, 476 loud rumbling noise. Three of the seismometers, recorded vibrations that occurred 477 during the primary calving event at this moment (Fig. 8). One of the stations was 478 deployed on the glacier surface, while the other two were well above the glacier, on 479 nearby land. From the seismic data collected, we were able to ascertain that the peak of 480 the calving event, the primary in a seismic sense, occurred at 06:37 UTC. Using cross-481 correlation of the seismic signals, we are able to determine the difference in arrival times, 482 and from this, estimate the calving location. In fact, two different methods are used to 483 estimate the calving event location, and they produce similar results, indicating the same 484 location on the northern glacier trunk. In the first method, travel times from all three 485 seismic stations are used simultaneously to find the most likely singular point of origin of 486 the calving signal, which is shown as the blue X (Fig. 9). In the second method, seismic 487 stations are used in only a pairwise sense and this results, instead of a point location, an 488 area as shown by the blue triangle (Fig. 9, details in Mei et al [2016]).

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From a TRI map of interferometric correlation (see again Fig. 5), we reported a precursor 491 event nearly an hour prior to the primary calving. The formation of this TRI surface 492 expression seems to be related to seismic activity around the same time (Fig. S7 in  493 Supp.). Evidence of precursory activity, from both TRI and seismic, gives us greater 494 confidence in asserting that calving is a process, made up of a number of punctuated 495 events. Calving of large ice masses may be a similar to earthquakes, in that earthquake 496 foreshocks sometimes culminate in much larger earthquakes. We note that there are also 497 several periods of high glaciogenic seismic energy visible on seismograms that do not 498 culminate into a large calving event. Detailed analysis of the high frequency on-ice 499 seismicity is the subject of ongoing study. 500 501 Parenthetically, the bedrock elevation of Helheim Glacier indicates that the bedrock is 502 deeper beneath the northern half of the trunk (Fig. 9), a fact that may be linked to where 503 the glacier preferentially calves, suggesting that a glacier grounded on deeper bedrock, 504 or the deeper portions of a calving front, may be more susceptible to calving. 505 506 3.5 TSUNAMETERS 507 508 Another way to track glacier activity is to monitor nearby ocean waves. These waves can 509 be excited by changes at the glacier front propagating subsequently into the ocean, or 510 vice versa, and thus have the potential to provide complementary information about the 511 calving process. 512 513 An array of seafloor moorings was deployed in Sermilik Fjord prior to our field campaign. 514 Tsunameters installed on each mooring were used to detect calving events in the fjord. 515 The tsunameters sampled every four seconds, which allowed for detection of the fast 516 barotropic waves traveling along the fjord. At the time of the primary August 12, 2014 517 event, two tsunameters were active with their locations shown in Fig.10a. The closer 518 one to the calving front was located about 70 km away at depth of 880 m, and the farther 519 one was 84 km away at depth of 908 m. 520 521 A propagating barotropic wave associated with each calving event was detected on both 522 active tsunameters (Fig. 10b). The signal of the primary calving event reached the 523 closest sensor between 6:51 and 6:53 UTC with amplitude of 10 cm. Approximately 160 524 seconds later the signal arrived at the farther one. Using a mean propagation speed of 525 calving waves in Sermilik Fjord, a barotropic signal generated at the calving front location 526 takes between 14.7 and 17.1 minutes to reach the closer sensor. This rough calculation 527 suggests the timing of the first calving event to be initiated sometime between 6:34 and 528 6:39 UTC.

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The smaller secondary event reached only one quarter of the amplitude of the primary 531 event and arrived at the closer tsunameter around 11:40 UTC, and at the farther one with 532 160 seconds lag again. The tsunameter data thus estimate the second event to be 533 initiated between 11:31 and 11:36 UTC, August 13. 534 535 The spectral and propagation characteristics of these waves are consistent with those of 536 other calving generated waves observed in Sermilik Fjord [Vaňková & Holland, 2016]. In 537 the cited study, a numerical model suggested that the effect of calving on the ocean is 538 equivalent to a damped oscillator boundary forcing with oscillation period between 5 to 10 539 minutes and damping time scale of 10 minutes. We conclude from our ocean-based 540 observations that in the instance of the calving events we observed in August, 2014, 541 calving created a wave response in the ocean, and not vice versa. We also note that 542 going forward, sea-floor tsunameter arrays are an effective way to monitor calving of an A cursory analysis of our AWS data (air temperature, radiation, wind, and precipitation) 551 did not reveal any obvious link to the observed calving events during our week-long 552 observation period, which is perhaps not surprising. From our AWS time-lapse cameras 553 (Fig. 3.11), we know the precise position of the calving front before and after the various 554 calving events. It is reassuring to find that the locus of the calving energy as determined 555 from the seismic data ( Fig. 3.9) is located near the calving front as revealed by the 556 camera images (Fig. 3.11). 557 558 The northern and southern trunks of the Helheim Glacier meet along a medial moraine, 559 evident in Fig 3.11 as a dark line consisting of rock and dust following along a flow line. 560 This suture zone, where two glacier streams meet, likely has a different structural 561 makeup than the ice elsewhere in either trunk, and we speculate that it plays a role in the 562 nature of the calving we witnessed (i.e. the secondary event occurred only over the 563 southern trunk) [Walker et al., 2015]. 564 565 Anecdotally, while flying over the glacier several days before the calving events we 566 noticed a significant amount of water collected in surface crevasses. Several days after 567 the calving events, we again flew over the glacier and noticed that most of the surface 568 water had disappeared. Our AWS cameras were not adequately positioned to show the 569 surface water and thus we are unable to say when the water drained and if it had any 570 possible relation to the calving events. 571 572 Our AWS camera was in operation prior to our field campaign and time-lapse over the 573 preceding year shows the aperiodic nature of the calving events at Helheim (Fig. S8 in  574 Supp.). It is evident from year-long time-lapse cameras, that the Helheim Glacier 575 generally advances in winter and retreats in summer, highlighting the fact that there is an 576 atmospheric influence on calving. The mechanism by which the atmosphere impacts 577 seasonal calving remains unclear, requiring further observational data. 578 579 580 4 TOWARD PARAMETERIZED CALVING 581 582 As mentioned earlier, our overarching goal is to develop a parameterization of calving. A 583 practical first step to this goal is to build a detailed process model, using theory motivated 584 by observations that can accurately simulate aspects of the calving process (see again 585 Figs. 5, 6). Such a process model is likely not suitable for use in a large-scale, long-586 simulation climate model, but can serve to guide the construction of a simplified 587 parameterization of calving to be used in a climate model. This parameterization goal is 588 well beyond the scope of the present work, in which we are only reporting on one 589 observation of calving, and our first steps towards detailed modeling of the phenomenon. 590 591 Glacier flow can only be accurately modeled provided one knows the rheology of the ice, 592 i.e. the relation between the strain rate and stress fields. The viscous rheology 593 appropriate to a slowly flowing glacier undergoing creep is relatively well known [Glen, 594 1958], as is the elastic rheology appropriate to bending [Timoshenko & Goodier, 1970]. 595 The plastic rheology that is perhaps appropriate to a fast moving glacier that is 596 undergoing fracturing and calving, such as Helheim Glacier, is unknown. Current 597 generation glacier models do not simulate calving in a realistic manner but progress is 598 being made by considering damage mechanics [e.g. Krug et al, 2014]. While such 599 models do describe the viscous and elastic behavior of glaciers based on an assumed 600 relation between strain (or strain rate) and stress, they do not yet describe the failure 601 associated with plastic flow, which is independent of strain and strain rate, complicating 602 matters greatly. Future modeling advancements, based on observations reported here 603 and elsewhere, should move forward the ability to model the plastic failure stress that 604 glaciers such as Helheim likely undergo. Specifically, our future observational efforts at 605 Helheim will be targeted at providing the data necessary to modify the glacier rheology to 606 include a plastic yield curve. This will be carried out following the analogous theoretical 607 framework, widely used in the sea-ice literature, successful in modeling sea-ice plastic 608 failure [Hibler, 1979].

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Based off an existing two-dimensional, along flow line model [Parizek et al., 2013] we 611 have begun to model the stress state of Helheim Glacier. As a starting point we are 612 simulating the viscous and elastic stress fields. When and where a glacier such as 613 Helheim ultimately fails depends not only on its material strength and the many 614 imperfections that limit it, but also on the crack-forming viscous (Fig. 12) and elastic ( Fig.  615 S9 in Supp.) differential stress field to which it is subjected as it completes its journey to 616 the ocean. Within a field of crevasses, theory indicates ~320 kPa of tensile stress is 617 necessary to generate new crevasses, with that threshold decreasing to ~30-80 kPa for 618 individual crevasses [van der Veen, 1998]. For a calving event to take place, surface 619 and/or basal crevasses must penetrate the full glacier thickness. In the viscous realm, 620 crevassing often takes place along lateral shear margins, where there are transitions in 621 basal topography and/or drag, and proximal to the ice-front where differences between 622 the glaciostatic and hydrostatic pressures across the interface lead to enhanced 623 deviatoric stresses within the ice that maintain the overall force balance. The glacier 624 surface steepens just downstream of regions with topographic highs and/or enhanced 625 basal drag to drive flow across these features, with the resulting changes in flow speed 626 leading to tensional longitudinal stresses within the glacier. Furthermore, tensional 627 stresses also develop across an onset region of an ice shelf or ice tongue as basal 628 traction vanishes where the base of the glacier loses contact with the solid earth. Finally, 629 within a few thicknesses or less of a marine-terminating glacier front, the stress state 630 within a glacier also favors failure due to the glaciostatic/hydrostatic pressure imbalance 631 between the glacier front and the combination of air and seawater into which it is flowing 632 (Fig. 12), as well as the tidal flexure of the floating tongue (Fig. S9 in Supp.). At this 633 stage, it is not yet clear from observation if any, some, or all of these detailed factors 634 need be included in a parameterization of calving. 635 636 While our modeling effort is currently aimed at a deterministic simulation of calving, as is 637 appropriate in the context of developing a process-oriented understanding of calving, it 638 may turn out in the long run that such a deterministic approach is not feasible in the 639 context of large-scale, long-simulation climate modeling. An alternative approach for a 640 calving parameterization has been to invoke a probability distribution, with calving 641 considered a random event drawn from an underlying distribution [Bassis, 2011]. The 642 empirical relationships or probability distributions appear to depend strongly on the 643 characteristics of a specific outlet glacier (bed slope, the presence of an ice shelf, 644 thickness above flotation, etc.). While we here present observations of just one calving 645 event and seek in the future to collect many more, there may be merit in the ultimate 646 parameterization of calving as a random event. Clearly, a large database of calving 647 events is required in order to build a viable probability distribution to give this approach a 648 significant foundation. This is also one of our long term goals.

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While calving has obvious relevance to glaciology, it is also germane to oceanography 651 albeit indirectly. This is particularly so in the context of freshwater release arising from where they melt, but even to arrive there it is important as a starting point to know where 656 icebergs are produced and what is their size distribution. The type of calving 657 parameterization we seek here through our future glaciological modeling efforts feeds 658 directly into this principal need in oceanographic modeling. 659 660