Earth and Planetary Science Letters 515 (2019) 283–290

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Earth and Planetary Science Letters

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Calving flux estimation from tsunami waves ∗ Masahiro Minowa a,b, , Evgeny A. Podolskiy c,d, Guillaume Jouvet e, Yvo Weidmann e, Daiki Sakakibara b,c, Shun Tsutaki f, Riccardo Genco g, Shin Sugiyama b a Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Valdivia, Chile b Institute of Low Temperature Science, Hokkaido University, Sapporo, Japan c Arctic Research Center, Hokkaido University, Sapporo, Japan d Global Institution for Collaborative Research and Education, Hokkaido University, Sapporo, Japan e Laboratory of Hydraulics, Hydrology and Glaciology, ETH Zürich, Zürich, Switzerland f Atmosphere and Ocean Research Institute, The University of Tokyo, Kashiwa, Japan g Dipartimento di Scienze della Terra, Università di Firenze, Florence, Italy a r t i c l e i n f o a b s t r a c t

Article history: Measuring glacier calving magnitude, frequency and location in high temporal resolution is necessary Received 13 November 2018 to understand mass loss mechanisms of ocean-terminating glaciers. We utilized calving-generated Received in revised form 14 February 2019 tsunami signals recorded with a pressure sensor for estimating the calving flux of Bowdoin Glacier Accepted 14 March 2019 in northwestern Greenland. We find a relationship between calving ice volume and wave amplitude. Available online 1 April 2019 This relationship was used to compute calving flux variation. The calving flux showed large spatial and Editor: J.P. Avouac − temporal fluctuations in July 2015 and in July 2016, with a mean flux of 2.3 ± 0.15 × 105 m3 d 1. Keywords: Calving flux was greater during periods of fast ice flow, high air temperature, and at low/falling tide, calving indicating the importance of increased longitudinal strain due to glacier acceleration and/or submarine glacier melting at the calving front. Long-term measurements with the method introduced here are promising Greenland for understanding the complex interplay of ice dynamics, melting and calving at glacier fronts. © 2019 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction coarse, and separating calving flux from submarine melting is dif- ficult. Ice discharge from outlet glaciers into the ocean accounts for In recent years, however, seismic measurements have been nearly half of the ice mass loss from the Greenland ice sheet (En- used to estimate calving flux and monitor the individual calving derlin et al., 2014). These glaciers have substantially retreated and events of ocean-terminating glaciers in Alaska (Bartholomaus et al., accelerated (e.g., Moon et al., 2012) under the influences of atmo- 2015), Svalbard (Köhler et al., 2016), and Greenland (Sergeant et spheric and oceanic warming (Holland et al., 2008). At the glacier al., 2016). For example, Bartholomaus et al. (2015)observed sea- front, ice mass loss occurs through frontal ablation composed of sonal to semi-diurnal variations in calving flux at Yahtse Glacier, two different physical processes: (i) calving due to mechanical Alaska by comparing passive seismic records with a calving inven- fracture of ice, and (ii) submarine melting controlled by thermody- tory, requiring tedious observation work. On a semi-diurnal time namic processes between ice and the ocean. Mass loss through the scale, tidal stresses at the calving front can influence calving rate, calving front, Q f, is commonly estimated from satellite image anal- whereas submarine melt rate modulates the calving rate on sea- ysis (e.g., Nuth et al., 2012; McNabb et al., 2015) with the equation sonal time scales at the glacier (Bartholomaus et al., 2015). Köh- below: ler et al. (2016)used a fifteen-year record of seismic signals to − estimate frontal ablation by comparing properties in seismic sig- dL = Q i Q f (1) nals with satellite-derived frontal ablation. They observed that a dt Af short-lived increase in frontal ablation was related to summer rain- where dL/dt is changes in glacier terminus position, Q is the i fall events, and seasonal peaks decayed within 1-2 months from terminus ice flux, and A is the cross sectional area of the termi- f the melt season maximum. However, mechanisms controlling the nus. However, temporal resolution using this method is relatively magnitude and the frequency of calving events are still under- investigated. Observations of glacier calving in high temporal and * Corresponding author. high spatial resolution are needed to understand the glacier mass E-mail address: [email protected] (M. Minowa). loss process from the glacier front. https://doi.org/10.1016/j.epsl.2019.03.023 0012-821X/© 2019 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 284 M. Minowa et al. / Earth and Planetary Science Letters 515 (2019) 283–290

Fig. 1. (a) Satellite image of Bowdoin Glacier in northwest Greenland, with instrument locations, and bathymetry in front of the glacier with contour intervals of 25 m. The background image was taken by Landsat 8 on 30 July 2016. (b) An example of ortho-image near the ice front obtained from UAV photogrammetry on 18 July, 2016. Blue triangles and orange circles indicate calving locations in July 2015 and July 2016 recorded by the time-lapse cameras during the field campaign. Black horizontal bar highlights the high-shear zone (Fig. S6). Calving flux histogram estimated from surface waves as a function of source-to-sensor distance with 200 m bins determined by Equation (3)in (c) July 2015 and in (d) July 2016. Gray shades highlight the location of subglacial discharge plumes which represent a mixture of subglacial freshwater and deep fjord water (Kanna et al., 2018).

Similar to seismic signals, surface-water waves have a great po- tem (GPS) derived ice speed and tide phases. This study proposes tential for monitoring glacier calving (e.g., MacAyeal et al., 2009; an inexpensive, but robust and accurate methodology for continu- Amundson et al., 2008, 2012). When an iceberg breaks off into the ous and long-term measurements of calving flux. water, surface-water waves move over the ocean or lake in front of calving glaciers, propagating away from the source (MacAyeal 2. Study site et al., 2009; Minowa et al., 2018). These waves are the most dis- ◦  ◦  tinctive surface-water waves in a fjord or a lake. In the case of Bowdoin Glacier (77 41 N, 68 35 W) is located 30 km north- large-scale calving events, the resulting waves can be destructive east of Qaanaaq in northwestern Greenland (Fig. 1). The glacier (Lüthi and Vieli, 2016). These tsunami waves have been used to discharges ice into Bowdoin Fjord through a 3-km wide calving detect and locate calving events, and to estimate calving ice vol- front. The height of the ice cliff above the ocean surface is be- umes (Minowa et al., 2018). In this previous study, a positive linear tween 30 and 50 m (Jouvet et al., 2017) (Fig. S7). South-eastern relationship was found between the calving ice volume and maxi- part of the ice cliff is ∼20 m higher than north-western part of mum wave amplitude of surface-water wave (Minowa et al., 2018). ice cliff due to shallow elevated bed rock (Sugiyama et al., 2015). However, calving ice volumes were estimated from time-lapse im- Water depth near the calving front in Bowdoin Glacier is deeper ages, leading to large uncertainties. To find a more robust relation- than 100 m, and further deepens to ∼250 m about 500 m from ship, it is necessary to quantify calving ice volumes with higher the north-western side of ice front (Fig. 1) (Asaji et al., 2018). Tidal ◦  ◦  precision. Recently, Unmanned Aerial Vehicle (UAV) photogramme- data at Pituffik/Thule (76 33 N, 68 52 W) showed 1–3 m of diurnal try has been providing Digital Elevation Models (DEMs) in high and semi-diurnal tidal amplitudes. These amplitudes and phase are spatial (∼cm) and temporal (∼day) resolutions to study ocean- very similar with the local tide gauge records used in this study terminating glaciers (e.g. Jouvet et al., 2017, 2018). Such DEMs can (r2 = 0.98). − be used to quantify calving ice volumes with unprecedented accu- The annual mean ice speed was approximately 200 ma 1 be- racy (e.g. compared to time-lapse image and human observation) fore 2000 (Sugiyama et al., 2015). Due to atmospheric/oceanic − (e.g. Bartholomaus et al., 2012; Minowa et al., 2018). warming, the glacier accelerated up to 500 ma 1 later on, and In this study, we measured the magnitude of surface-water experienced a rapid retreat of 2 km between 2008 and 2013 waves generated by calving events at Bowdoin Glacier, an ocean- (Sugiyama et al., 2015). In the meantime, substantial glacier thin- − terminating glacier in northwestern Greenland (Fig. 1). Glacier ning of 4.1 ma 1 was observed. It was estimated that 60% of the calving was also monitored by time-lapse imagery and quantified thinning was controlled by glacier dynamics (Tsutaki et al., 2016). by high-resolution DEMs derived from UAV photogrammetry. Sur- Since 2013, the ice-front position has been relatively stable (Tsu- face wave properties were compared with calving ice volumes to taki et al., 2016; Sakakibara and Sugiyama, 2018). infer calving flux during July 2015 and July 2016. To further in- Bowdoin glacier dynamics on a daily-to-weekly scale resolution vestigate the mechanisms controlling calving, we compared the was documented by GPS, seismic measurements and UAV pho- calculated calving flux with air temperature, global positioning sys- togrammetry (Sugiyama et al., 2015; Podolskiy et al., 2016; Jouvet M. Minowa et al. / Earth and Planetary Science Letters 515 (2019) 283–290 285 et al., 2017). Glacier surface speed was found to be very sensi- 3.2. UAV photogrammetry tive to small perturbations in ice surface melt rate, precipitation, and tide (Sugiyama et al., 2015). Since acceleration was more pro- High-resolution ortho-images and DEMs were produced from nounced near the ice front, it led to larger longitudinal strain rate images collected by UAV in July 2015 (Skywalker X8) and July during the period (Sugiyama et al., 2015). Seismic observations 2016 (Firefly6) (Jouvet et al., 2017, 2018). The UAV surveyed Bow- near the glacier front revealed that frequency of icequakes was doin Glacier twice in July 2015, and more than 20 times in July controlled by the longitudinal strain rate of the glacier (Podolskiy 2016 (Fig. 1). The pictures of each flight were post-processed by et al., 2016). The strain rate increased due to acceleration dur- structure-from-motion with Agisoft PhotoScan software. As a re- ing falling tide and led to intense surface crevassing (Podolskiy et sult, 0.25 m and 0.5 m resolution ortho-image and DEMs of the al., 2016). This suggested that hydrostatic pressure action on the calving front were reconstructed for each flight in 2015 and 2016, glacier front played a first-order role in the diurnal speed varia- respectively. Further details about UAV flights, and data processing tions, and the resulting calving activity. are elaborated on Jouvet et al. (2017, 2018). In total, 27 calving ice volumes were quantified by differen- 3. Data and methods tiating nine high-resolution DEMs using geographic information system software (QGIS). The pair of DEMs and number of calv- 3.1. Surface-water wave measurements ing ice volumes quantified by differentiation are summarized in Table S1. The accuracy of the measurement was evaluated using el- evation changes over off-glacier terrain, where elevation change is We observed fjord surface waves by operating a water pres- assumed to be zero. The error evaluation was performed for each sure sensor (HOBO U20, Onset Co. in 11–20 July 2015 and AR4500 pair of DEMs. The root-mean-square varied from 0.11 × 102 m3 piezometer, Geokon in 15–29 July 2016). The methods followed to 1.37 × 103 m3, which is several orders of magnitude smaller those in Minowa et al. (2018). The sensor was installed on the than the volume of observed calving events. In order to calcu- coast of Bowdoin Fjord, 100 m from the eastern margin of the late each calving ice volumes, we made sure that there were no glacier calving front (Fig. 1a). The sensor was mounted in a other calving events between the DEMs. Our method was not able 2-m long aluminum pipe, which was safely anchored to boulders to measure the volume of ice detached in the water, but the oc- (Fig. S1). The sensor was installed in the ocean at low tide (during currence of submarine calving was very limited according to the spring tide), so that it remained in water during the observation time-lapse images. periods. The distance from the sensor to the ice front ranged from 100 to 3000 m (Fig. 1). The fjord was free of ice-mélange during 3.3. Time-lapse imagery our observation periods in July 2015 and July 2016. Water pressure was recorded at 0.5 Hz in 2015 and at 20 Hz in 2016. Thus, the corresponding highest observable Nyquist frequencies were 0.25 Time-lapse cameras continuously photographed the glacier front during the field campaigns in 2015 and 2016. In 2015, we and 10 Hz, respectively. The water pressure P w was converted to used an automatic camera (GoPro HERO3, 3000 × 2250 pixels) on water level Hw by correcting for atmospheric pressure variations, the bedrock near the glacier front (Fig. 1a). In 2016, two automatic Hw = (Pw − Pa)/ρw g, where ρw, g and Pa are the density of sea- − − × water (1025 kg m 3), gravitational acceleration (9.81 m s 2), and cameras (GoPro HERO3 and GARMIN, VIRB X, 3000 2250 pixels) air pressure measured with a local weather station at Qaanaaq Air- were used alternately, to reduce the risk of losing images dur- port located 30 km southwest from the glacier. Due to the limited ing the battery replacement or due to device failure (Fig. 1a). The duration of air pressure measurement at the glacier, we used the GoPro and GARMIN took images every 10 and 4 s by using cam- record observed at Qaanaaq. Both data-sets were well correlated era software, respectively. Power supply was provided by a 12 V (r2 = 0.99). The accuracy of the sensor was equivalent to a water battery and a solar panel. The midnight sun enabled us to take level of ±5 mm with a resolution of 1.4 mm in 2015, and ±5 mm photographs continuously 24 hours a day during the field cam- with a resolution of 1.2 mm in 2016, respectively. After correcting paigns (9–20 July 2015, 5–21 July 2016). We utilized this time-lapse imagery to identify calving events. for atmospheric pressure variations, we applied a high-pass filter We firstly made a movie from the time-lapse imagery for the with a cut-off period of 1 h to remove tidal signal (Fig. S2). whole period and then observed calving events and their style by Surface-water waves associated with glacier calving were iden- visual inspection. The identified events were located more accu- tified by defining a wave-height threshold following the method rately on UAV ortho-images based on distinctive features such as presented by Minowa et al. (2018). We detected each calving event large crevasses, plumes near the ice front, and ice cliff geome- by identifying a signal with an amplitude >0.05 m. The 0.05 m try using a geographic information system software (Fig. 1). It is threshold was chosen by comparing waves with time-lapse images, necessary to note how we define a calving event, since calving is and using the maximum likelihood algorithm from Powers (2011). sometimes a phenomenon with a series of several sizes of iceberg In order to investigate the accuracy of this detection method, a collapse. Even if some events could be composed of several calv- number of events were obtained from surface waves and time- ing events, the most of icebergs broke off as a single calving event, lapse imagery. The estimator was based on “F-score” which maxi- which generated the corresponding surface-water waves (Supple- mizes the true-positive detection and minimizes the false-negative mental Movie). Any rare case of a calving sequence was recognized detection (as detailed in SI). With the 0.05 m threshold, we detect as one calving event for a sake of simplicity and since the wave 109 events in total in 2016. There were 15 false-positive and 20 was dominated by the largest block. false-negative events. For the chosen threshold, the corresponding precision, recall and F-score were 0.83, 0.79 and 0.82, respectively (Powers, 2011) (Fig. S3). Both false-positive and negative detec- 3.4. Correction for wave amplitude tions were associated with small calving events. The mean wave height of false-positive detection was 0.09 m, which is close to the In order to explore the relationship between calving ice volume threshold. These events were generated by small calving events, and wave properties, we compared the calving ice volume with which were difficult to identify using the time-lapse sequence. On maximum wave amplitude, Hmax, and corrected maximum am- the other hand, some of the small calving events identified by the plitude, Hmax-n, described below. For correcting wave amplitude, time-lapse images were hard to detect from surface waves. we assumed that there were two possibilities to observe different 286 M. Minowa et al. / Earth and Planetary Science Letters 515 (2019) 283–290

Fig. 2. (a) Schematic illustration of tsunami measurement. DEM before (b) and after (c) the calving event on 18 July 2016, 750 m from the pressure sensor. The red curves indicate the ice detached by this event. (d) Low-pass-filtered (<0.25 Hz) surface waves generated by the calving, (e) spectrogram of the waves with a moving window of 20 s and an overlap of 90%, and (f) power spectrum density. The gray dashed line highlights a relationship between the peak frequency and source distance estimated by Equation (3) (720 m). The gray dashed horizontal line indicates median frequency.

Hmax while it was same size as the iceberg. i) Since wave am- et al., 2009). Therefore, it is possible to estimate the source-to- plitude decays with distance over the water surface, Hmax can be sensor distance from surface-wave observations alone (MacAyeal larger when calving occurs close to the sensor. ii) Since the poten- et al., 2009; Minowa et al., 2018) via the formula: tial energy of an iceberg can be different depending on the ice cliff df g height, Hmax can be larger when calving occurs from a higher ice = , (3) dt 4π cliff. These assumptions were taken into account: e where t (s) is the arrival time of a wave with a frequency f (Hz). 1/2 Hmax-n = (Hmax × e )/0.5h, (2) Equation (3)was used to determine e (m) from df /dt, which 1/2 was obtained by fitting a linear relationship to the peak frequency where e is geometric attenuation in surface-wave amplitude in the spectrogram. Further method details are given in Minowa dependent on the estimated source-to-sensor distance, e (m) et al. (2018). Accuracy of e was evaluated by comparing the dis- (Podolskiy and Walter, 2016). h (m) is the ice cliff height of the tance measured with the time-lapse images and UAV imagery, m. glacier derived from the DEMs (Fig. S7). The factor 0.5 is a simpli- Uncertainties of e were estimated to within 9.5% of m by cal- fied way to assume the height of the center of mass from the top culating the root-mean-square error between e and m (Fig. S5). ice surface (Fig. 2a). We estimated the source-to-sensor distance e from a spec- 3.5. Ice surface speed trogram, which is the result of a Fourier Transform (Fig. 2f). The arrival time of a surface wave can be assumed to be linearly de- GPS ice speed measurements were carried out 1.7 km upstream pendent on the wave frequency for deep water waves (MacAyeal of the glacier front (Fig. 1a). Data was collected using a dual M. Minowa et al. / Earth and Planetary Science Letters 515 (2019) 283–290 287

Fig. 3. (a) Distribution of calving ice volume calculated from the DEM comparison. Gray bars and black circles indicate fraction of calving ice volume and cumulative calving ice volume, respectively. Scatter plots for calving ice size versus (b) maximum amplitude, and (c) corrected maximum amplitude. Gray solid lines indicate a best-fit regression model on the data, and gray dotted lines show spans of 95% confidence level, respectively. Dashed line indicates best-fit regression model after excluding outliers more than one standard deviation out. Horizontal error bars indicate a possible error arising from the uncertainties in the source-to-sensor distance and the ice cliff height in Equation (2). frequency GPS (GNSS Technology Inc, GEM-1), with a base sta- 4.2. Calving ice volume tion located on the bedrock near the glacier about 1.2 km from the GPS installed on the glacier. A GPS antenna was mounted In total, 27 calving events were utilized to calculate the loss of on an aluminum pole drilled into the glacier, and a receiver ice volume by comparing DEMs generated by UAV photogramme- continuously recorded GPS signals with a sampling rate of 1 s. try (Fig. 2b and c). Fig. 3a shows a histogram of calculated calving Three-dimensional coordinates of the pole were obtained by post- ice volume V c. The calving ice volume ranged from a minimum of 2 3 4 3 processing the data with the static positioning technique using 3.5 × 10 m to the maximum of 4.9 × 10 m , with a mean × 4 3 GPS processing software RTKLIB. With the relatively short baseline V c of 1.2 10 m . These numbers were consistent with previ- length (∼3 km), positioning error in the static GPS measurement ous studies on relatively small, grounded calving glaciers in Alaska is typically several millimeters in the horizontal direction. Hori- (Bartholomaus et al., 2012), Svalbard (Chapuis and Tetzlaff, 2014), zontal ice speed was computed by filtering a time series of the the Antarctic Peninsula (Petlicki and Kinnard, 2016) and southern positioning data using a Gaussian smoothing algorithm with a time Patagonia (Minowa et al., 2018). While a fraction of the smallest × 4 3 window of 3 hours (Sugiyama et al., 2015). calving class (<1 10 m ) accounted for 70% of the quantified events, their cumulative calving ice volume accounted only for 27% of the total (Fig. 3a). In contrast to this, the largest class (>4 × 104 4. Results m3) (7% of total number of events) accounted for 30% of the total quantified volume.

4.1. Surface-water waves 4.3. Time-lapse imagery

Fig. 2 shows an example of surface waves generated by a A total of 185 calving events were identified by visual inspec- subaerial-calving event, a drop of a 50-m-long ice block into the tion of time-lapse camera images and manually localized on cor- fjord at the location of 750 m from the sensor (Figs. 2b and c). responding UAV imagery (Fig. 1b). These events are non-uniformly The generated wave had a long and low positive onset centered distributed along the calving front. Both in 2015 and 2016, a large at 150 s (Fig. 2d). The amplitude decreased gradually over ap- number of events clustered above the plumes (Fig. 1b), indicat- ing a probable local enhancement of subglacial melt (e.g., Fried et proximately 150 s after the maximum wave amplitude of 0.18 m. al., 2015; Rignot et al., 2015). Among the 185 events, we recorded Low frequency surface waves (0.03 Hz) arrived at the sensor first, only subaerial calving events. No subaqueous calving was observed followed by higher frequency waves up to 0.25 Hz (Fig. 2e), sug- during the operational time period of the water pressure sen- gesting our deep-water assumption was correct. This corresponds sor. to the frequency dispersion of multiple-frequency waves of micro- tsunamis observed in Antarctica by MacAyeal et al. (2006, 2009) 5. Discussion and in Patagonia by Minowa et al. (2018). The peak amplitude of the wave was found at a frequency of 0.06 Hz, with relatively 5.1. Calving flux calculated from surface-water waves strong power between 0.02 and 0.15 Hz (Fig. 2f). By applying the criteria of calving-generated waves described − The calving volumes quantified by the DEM’s differentiation of in the Methods section, we detected 107 events (11 d 1) and 205 − the 27 events were compared with surface-water waves properties events (15 d 1) during the observation periods in July 2015 and (Fig. 3). We find a positive correlation between maximum ampli- July 2016, respectively (Fig. S2). A slightly higher calving rate was tude and calving ice volume. The correlation was more significant observed in July 2016, but the mean maximum amplitudes were after applying the correction defined by Equation (2)(Fig.3c). Are- similar for both periods: 0.17 m in 2015 and 0.16 m in 2016. The lationship between the corrected maximum amplitude and calving time distribution of these events was highly irregular. For example, 3 a greater number of events were detected on July 18 and 19, 2015, volume (m ) was obtained by linear regression leading to and on July 20 and 26, 2016 (Fig. S2). V = (1.3 × 105)H − 9.3 × 103. (4) Fig. S4 shows cumulative distribution functions of waiting time c max-n τ (min) in comparison to best-fit power-law and exponential mod- By applying Equation (4)to all surface-water wave records, we els. The waiting time, τ , spans by more than one order of mag- estimated calving flux of Bowdoin Glacier in July 2015 and July nitude, between 0.35 and 959 min. The exponential distribution 2016 (Fig. 4). Details on error estimation of the model were de- model reproduced the data better than power-law in both periods scribed in SI. Fig. 5a shows a cumulative distribution function 2 = 2 = (rexp 0.86 and rpow 0.56) (Fig. S4). of the estimated calving ice volume V c. The calving ice volume 288 M. Minowa et al. / Earth and Planetary Science Letters 515 (2019) 283–290

Fig. 4. Calving flux (blue bars) relative to the mean flux estimated from surface-water waves in (a) July 2015 and (b) July 2016. Red and black lines indicate the air temperature measured at Qaanaaq airport located 30 km southwest from the glacier and ice surface speed, respectively.

UAV-derived calving flux, Q c-uav, agreed well with Q c-wave: Q c-uav 5 3 −1 5 3 = 1.61 ± 0.06 × 10 m d and Q c-wave = 1.74 ± 0.12 × 10 m −1 5 d between 11–16 July 2015, while Q c-uav = 1.70 ± 0.06 × 10 3 −1 5 3 −1 m d and Q c-wave = 1.86 ± 0.11 × 10 m d between 15–18 July 2016 (Table S1). Secondly, over the entire time the pressure sensor was operational in 2015 and 2016, we estimated Q c-wave to − be 1.99 ± 0.14 × 105 m3 d 1 in 2015 and 2.5 ± 0.15 × 105 m3 − d 1 in 2016. Assuming that the ice front below the ocean surface has the same calving rate as the subaerial portion, frontal ablation was 8.3 − − ± 0.6 × 105 m3 d 1 in 2015 and 8.9 ± 0.6 × 105 m3 d 1 in 2016 (Table S1). These numbers were approximately 5 times larger than Q c-wave. This is because 86–89% of the entire ice front is under the ocean surface (Sugiyama et al., 2015). Our time-lapse imagery in- dicated that the dominant type of calving was subaerial calving, whereas no submarine calving was observed. This might be due to under-sampling with the chosen time-resolution of our time- lapse imagery. In fact, there were several small-amplitude waves which could not be associated with any features of time-lapse im- agery. However, submarine calving event is usually composed of a single large piece of ice (Minowa et al., 2018), which should be detectable with our time-lapse cameras (e.g., on July 13, 2016 Fig. 5. (a) Distribution of calving ice volume (with 3 × 103 m3 bins; log-log scale) we observed one, but it occurred before the deployment of the of all data obtained during the two field campaigns. Blue solid and orange dashed pressure sensor). Consequently, the substantial difference between lines indicate best-fit power and exponential distribution models. (b) Colored mark- ers indicate histogram of calving rates depending on tide phases. The total number our estimated calving flux and the frontal ablation inferred by UAV of calving events were divided with the duration of each tide phases. Gray stair in- analysis suggests that submarine melting played a first-order role dicates histogram of cumulative calving ice volume estimated from the corrected in the frontal erosion of Bowdoin Glacier during the study period. wave amplitude. This is even more pronounced near the plumes (Fig. 1). Submarine melt undercuts the ice front under the water surface as reported ranged from a minimum of 1.0 × 104 m3 to a maximum of 7.6 × at ocean-terminating glaciers in western Greenland (Fried et al., 104 m3, with a mean V of 1.7 × 104 m3. These numbers are sim- c 2015; Rignot et al., 2015), with the consequence of enhanced sub- ilar to previous studies (Bartholomaus et al., 2015; Chapuis and aerial calving in the vicinity of meltwater plumes (Bartholomaus Tetzlaff, 2014; Petlicki and Kinnard, 2016; Minowa et al., 2018). et al., 2013; Fried et al., 2018). However, the partitioning between The distribution of calving ice volume was reproduced best by an calving and submarine melting remains unclear. For instance, Jou- exponential model and to a slightly lower extent by the power law (Fig. 5a). vet et al. (2017)found – by means of numerical modeling – that a Table S2 summarizes calving flux estimated from the surface large-scale event observed at Bowdoin Glacier, was likely triggered waves and individual values used to calculate the calving flux and by a half-thickness deep crack, suggesting that major submarine the frontal ablation derived from UAV image analysis based on ice loss at Bowdoin Glacier might be mechanical. Long-term mea- Equation (1)(see SI text S2). First, we calculated mean daily calv- surement of water surface waves is necessary to further investigate ing flux Q c-wave from 11 to 16 July 2015 and from 15 to 18 July the partition of calving and submarine melting, and their spatial 2016 in order to compare those derived from UAV. As a result, and temporal variability. M. Minowa et al. / Earth and Planetary Science Letters 515 (2019) 283–290 289

5.2. Variations in calving flux compared to air temperature, ice speed maximum wave amplitude. Using that relationship, we estimated − and tide calving flux to be 1.99 ± 0.14 × 105 m3 d 1 in July 2015 and 2.5 − ± 0.15 × 105 m3 d 1 in July 2016, which agreed well with UAV- The estimated calving flux varied substantially over time in derived calving flux. We also compared estimated calving flux with both periods (Figs. 4a and b). For instance, it was relatively large UAV-derived frontal ablation, which was only 20% of the frontal ab- on the 12th and 19–20th of July 2015 (Fig. 4a), and on the 20th, lation at Bowdoin Glacier during the summer field campaigns. 22–23th, and 26th of July 2016 (Fig. 4b). These periods correspond Calving rate co-varied with air temperature, ice speed and tide to high air temperature and fast ice flow (Figs. 4a and b). In ad- phase. A high calving rate was associated with high tempera- dition to this, time-lapse records indicated that the calving events ture and ice speed. Our analysis suggested that calving events clustered near the plumes or the high-shear zone (Figs. 1b and d). were clustered near the plumes and the high shear zone. An in- These results suggest two main driving mechanisms of the calv- crease of shearing and submarine melting can explain the local- ing at Bowdoin Glacier: (i) Short-term ice dynamics is controlled ized increase of the calving rate. Relatively high calving rate was by basal water pressure produced by meltwater or precipitation also observed during low and falling tide. This study was based input to the base of the glacier (Sugiyama et al., 2015). Increas- on a relatively short time frame of measurements, and laborious ing air temperature enhances ice melting, leading to an increase UAV-photogrammetry and visual inspection of time-lapse imagery. of meltwater input at the glacier base. Increased ice speed results However, after such a training period, the novel methodology, in- in greater longitudinal stain rate (Podolskiy et al., 2016), which troduced here, is possible to apply to long-term observations on increases fracture of the glacier, particularly near the shear zone ice-water interaction at calving glaciers. In particular, it is impor- (Jouvet et al., 2017) (Fig. S6). This explains why we observed larger tant to understand how ice-mélange could modify the tsunami calving flux and higher ice speeds on warmer days. (ii) Submarine signals or how rare but large-scale calving (Jouvet et al., 2017) melting is known to trigger subaerial calving events (e.g. Motyka could shift the partitioning of the frontal ablation. et al., 2003). Theoretical and modeling studies have found that the submarine melt rate at a glacier front is dependent on subglacial Acknowledgements discharge and ambient seawater temperature (Jenkins, 2011; Xu et al., 2012; Sciascia et al., 2013). Therefore, increased subglacial We thank field members of the campaigns in 2015 and 2016. discharge due to warm air temperature might have enhanced sub- Bathymetry data was provided by Shintaro Yamasaki and Izumi marine melting, and in turn triggered subaerial calving as observed Asaji. We thank Matthias Scheiter for his comments on the early in our data. manuscript. The manuscript was handled by Scientific Editor, Jean- In order to investigate the relationship between calving rate Philippe Avouac, and carefully reviewed by Martin Lüthi and an and tide, we compared the frequency of calving events with semi- anonymous reviewer. This work was a part of the GRENE Arc- diurnal tide phases: rising, falling, high and low tides. Following tic Climate Change Research Project and partially carried out in the previous study by Bartholomaus et al. (2015), we consider the Arctic Challenge for Sustainability (ArCS) project. Masahiro high- and low-tide calving to be those events that occur within Minowa was supported by Grant-in-Aid for JSPS Research Fellow an hour of the semi-diurnal maxima and minima. Otherwise, calv- JP16J01860 and by the ArCS fellowship for Japanese early car- ing events are classified as occurring during rising and falling tides. rier scientist and graduate students. Surface-water waves and data The highest calving rate was observed during falling and low tide presented in the study can be obtained from zenodo data deposi- (Fig. 5b). The mean calving rate was 4.2, 4.1, 3.7 and 2.4 events tory (http://doi .org /10 .5281 /zenodo .1432894). Landsat images, tide − d 1 for low, falling, rising and high tide, respectively. During high records and air temperature records were downloaded from http:// tide, the calving rate was half of other tide phases (Fig. 5b). We earthexplorer.usgs .gov, http://www.ioc -sealevelmonitoring .org, and investigated further whether this discrepancy depends on calving https://gis .ncdc .noaa .gov, respectively. ice volume, and similar trends were observed irrespective of calv- ing ice volume. However, presumably due to the small number of Appendix A. Supplementary material samples, these differences are not significant for the largest calv- ing ice volumes (Fig. 5b). At ocean-terminating glaciers in Alaska Supplementary material related to this article can be found on- and Svalbard, it was reported that diurnal and semi-diurnal calving line at https://doi .org /10 .1016 /j .epsl .2019 .03 .023. flux was modulated by tide (Bartholomaus et al., 2015; Koubova, 2015). A high calving rate was previously reported during low References and falling tide at Yahtse Glacier in Alaska (Bartholomaus et al., 2015). However, this relationship was not observed in previous Amundson, J.M., Truffer, M., Lüthi, M., Fahnestock, M., West, M., Motyka, R., 2008. studies (Qamar, 1988; O’Neel et al., 2003, 2007, 2010). At Bowdoin Glacier, fjord, and seismic response to recent large calving events, Jakob- shavn Isbræ, Greenland. Geophys. Res. Lett. 35 (22). https://doi .org /10 .1029 / Glacier, the higher number of calving events during low and falling 2008GL035281. tide is consistent with the observations about the tide-modulated Amundson, J.M., Clinton, J.F., Fahnestock, M., Truffer, M., Lüthi, M.P., Motyka, R.J., ice speed and ice quakes (Sugiyama et al., 2015; Podolskiy et al., 2012. Observing calving-generated ocean waves with coastal broadband seis- 2016). Hydrostatic pressure acting on the calving front modulates mometers, Jakobshavn Isbræ, Greenland. Ann. Glaciol. 53 (60), 79–84. https:// doi .org /10 .3189 /2012 /AoG60A200. ice speed as well as icequakes facilitating ice fracturing, and thus Asaji, I., Sakakibara, D., Yamasaki, S., Sugiyama, S., 2018. Rapid retreat of Bowdoin glacier calving. Glacier in northwestern Greenland controlled by the ocean and glacier bed ge- ometry. Abstract (C21B-1323) presented at 2018 AGU Fall Meeting, Washington, 6. Conclusions D.C., 10–14 Dec. Bartholomaus, T., Larsen, C., O’Neel, S., West, M., 2012. Calving seismicity from iceberg–sea surface interactions. J. Geophys. Res., Earth Surf. 117 (F4), 389–399. We observed calving-generated tsunamis using a pressure sen- https://doi .org /10 .1029 /2012JF002513. sor installed in front of an ocean-terminating glacier in northwest Bartholomaus, T.C., Larsen, C.F., O’Neel, S., 2013. Does calving matter? Evidence for Greenland. The surface-wave measurements were accompanied by significant submarine melt. Earth Planet. Sci. Lett. 380, 21–30. https://doi .org / UAV and time-lapse photography. UAV-derived DEMs are used to 10 .1016 /j .epsl .2013 .08 .014. Bartholomaus, T., Larsen, C.F., West, M.E., O’Neel, S., Pettit, E.C., Truffer, M., 2015. quantify calving ice volume. In total, 27 individual calving events Tidal and seasonal variations in calving flux observed with passive seismol- were captured by UAV derived DEMs and their volumes quanti- ogy. J. Geophys. 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