The site for this study is Hansbreen, a retreating, grounded, polythermal tidewater glacier terminating in Hornsund fjord, Svalbard. Its calving mode, believed to be driven by melt undercutting and many relatively small calving events from above the water surface (Pętlicki et al., 2015), provides a challenging test case for camera and satellite estimates of mass flux.

A map of the study site and an example photograph of the terminus of Hansbreen are shown in Fig. 1. Hansbreen covers an area of around 54 km², is more than 15 km long (Błaszczyk et al., 2013), and has a 1.5 km wide active calving front with an average height of around 40 m (Błaszczyk et al., 2009, 2021), which is approximately 30 %–40 % of the total ice thickness. The glacier surface flow is dominated by basal motion in the ablation area (Vieli et al., 2004), and the mean annual flow velocity near the terminus and its calving flux is estimated to be 177 m yr⁻¹ and 35×10⁶ m³ yr⁻¹, respectively (Błaszczyk et al., 2019).

Figure 1(a) Map of the study site and (b) example image of the Hansbreen terminus. Locations of the time-lapse camera and the acoustic buoy are marked with yellow and white font, respectively. The map is in UTM projection system (zone 33N). The dashed black lines show different propagation transects that were used for estimating the noise transmission loss. Landsat 8 satellite data collected on 11 September 2013, courtesy of the US Geological Survey, Department of the Interior. Bathymetric data provided by (1) the Norwegian Hydrographic Service under the permit no. 13/G722, issued to the Institute of Geophysics Polish Academy of Sciences, and (2) the Faculty of Natural Sciences, Institute of Earth Sciences, University of Silesia in Katowice, Sosnowiec, Poland (Błaszczyk et al., 2021).

Both glacial behavior (Pętlicki et al., 2015; Błaszczyk et al., 2021) and the propagation of calving sounds (Glowacki et al., 2016) are sensitive to the space and time-varying thermohaline structure of water masses in the bay, which were characterized with CTD casts. The water temperature and salinity (practical salinity units) in the center of the bay ranged from −1.8 to more than 2.0 ^∘C and from 30 to almost 35 during 2015 and 2016 (Moskalik et al., 2018). Sound propagation also depends on water depth, which drops to almost 100 m along a transect parallel to the glacier terminus (see Fig. 1a). The morphology of the bay varies greatly, with numerous moraines and flat areas created during the retreat of Hansbreen (Moskalik et al., 2018).

Glowacki and Deane (2020) have shown that the mass of individual icebergs can be estimated from the sound they produce when they impact the sea surface. In that study, 169 subaerial calving events from Hansbreen were manually identified in time-lapse photography and simultaneous recordings of the ambient sound, both made roughly 1 km from the glacier terminus. Despite significant variability in the total sound energy produced by an impact event for icebergs of comparable size, Monte Carlo simulations of ensemble time series show that accurate estimates of subaerial calving flux can be made if sufficient events are averaged (40 events for 20 % standard error for Hansbreen).

The manual identification of calving events using time-lapse photography and underwater sound is accurate but too labor intensive to be seriously considered for long-term datasets. This issue is addressed here by developing algorithms for the automatic detection of ice impact noise in the ambient sound recordings and rejection of interfering events, such as the disintegration of icebergs in the bay to obtain accurate estimates of ice loss from the terminus of Hansbreen due to calving.

The automatic detection of calving events is based on the observation that the ambient sound field in a glacial bay is composed of two distinct categories of sound sources: (1) sources that radiate noise with statistical properties that are stationary on the timescale of a calving event (such as melting glacier ice, for example) and (2) transient sources, like calving, superposed on this stationary background. During periods when noise in the bay is dominated by ice melting and calving, the signal during a 10 min data segment has the form of a wandering baseline punctuated at random intervals by hill-shaped increases as calving events occur. The level and noisiness of the baseline varies over time due to changes in the rate of ice melting on the glacier terminus, proximity to the hydrophone of icebergs drifting in the bay, and variable acoustic propagation through the bay. These varying conditions are unpredictable and require the selection of a baseline level and event detection threshold that is adaptable.

The signal processing scheme for event detection works as follows. A 10 min segment of ambient sound is transformed into a spectrogram. The sound power, P_b, between a lower and upper frequency band, f₀=30 Hz to f₁=100 Hz, is then computed using

where P_xx is the power spectral density estimate for the noise segment and the operators M(Θ) and B(Ω) are the filters described below. The selection of frequency limits is motivated by previous analyses of the calving noise presented in Glowacki and Deane (2020) and Glowacki (2020) (see Appendix A: Materials and methods for more details). The integral in Eq. (1) is calculated using the trapezoidal rule. The filter M(Θ) is a median filter of the order of Θ=7 and is useful for eliminating loud, impulsive noise sources that are too short to be calving noise. A boxcar filter B(Ω) of length Ω=32 points is applied to further reduce the effects of impulsive noise sources and random variations in noise power.

A baseline power for the noise in the absence of calving, P_base, is taken to be the median of the probability density distribution of P_b. A threshold of detection, P_thres, is then selected to be 1.5 times the largest value of P_b with relative likelihood

where β=5. This constant plays a central role in detector performance and is referred to as the “detection factor”. It should be borne in mind, however, that different study sites and experiment geometries may require different constants and thresholds for effective calving detection (see Appendix A: Materials and methods).

Calving events are identified as continuous periods of time when P_b exceeds P_thres. The detection algorithm is based on the idea that calving events are relatively rare within 10 min intervals, and periods of time containing many successive events will drive the algorithm to select only the most energetic of them (see Appendix A: Materials and methods).

An example of the detector output is shown in Fig. 2. Figure 2a shows 1 min of ambient sound energy containing a calving event, presented in dB re 1 µPa² Hz⁻¹ as a function of frequency and time. Figure 2b shows the output from the band-pass and median filters, the baseline level, the threshold level, and detection of the calving event. The detector was run on the 26 d of recordings, resulting in the detection of 4258 events (see Appendix A: Materials and methods for a discussion of how sensitive the algorithm is to the choice of detection factor). The primary outputs of the event detector are the event start and end times, t₀ and t₁.

Figure 2Calving detector explained. (a) A spectrogram of the sound produced by a calving event within the background noise radiated by the melting terminus of Hansbreen. The frequencies f₀ and f₁ on the right-hand side of the plot denote the lower and upper limits of the detection frequencies (see text for details). (b) Noise power from the spectrogram above, integrated from f₀ to f₁ and filtered. The calving event is detected when the noise power exceeds the power threshold, P_thres, as annotated by t₀ and t₁. The threshold power is based on the baseline power, P_base, which is determined from a statistical analysis of the sound (see text for details).

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The problem remains of identifying events that were detected as calving but which are not. Visual inspection of noise spectrograms combined with listening to the corresponding sound recordings revealed two major sources of interfering sounds: (1) the disintegration of icebergs close to the acoustic buoy, which sounds like a calving event because the iceberg sheds blocks of ice into the water as it disintegrates, and (2) water movement around the hydrophone (flow noise). Other interfering events include calving from the terminus with highly energetic contacts between the falling iceberg and the terminus, icebergs colliding with other ice pieces that occupy the sea surface along the terminus, and calving events involving ice block rotation in the air, resulting in large contact area between the iceberg and sea surface leading to atypical sound production. Although all these events represent a challenge for the technique, the most concerning are the flow noise and disintegrating icebergs, which can be confused with very large calving events. The interfering events must be removed from the calving inventory before the ice mass loss is estimated. To deal with the misclassification problem, we take two steps.

First, we take advantage of the fact that submarine melting of glacier ice also generates underwater noise due to the impulsive release of pressurized air bubbles into the water (Urick, 1971; Deane et al., 2014; Pettit et al., 2015). Glowacki et al. (2018) have demonstrated that the melt noise has an α-stable distribution. This should not come as a surprise as stable distributions allow skewness and heavy tails (Nolan, 2021). Importantly, the characteristic exponent of the α-stable distribution – a parameter that determines the heaviness of the tails – indicates proximity to a melting source. When the melting iceberg is close to the receiver, the underwater noise at frequencies 1–10 kHz is more impulsive and the exponent α deviates from 2. Here, we assume the following: if α<1.95 for the noise segment immediately preceding the calving noise, there is a high likelihood that the corresponding event detected by the automated algorithm is in fact an iceberg disintegrating close to the hydrophone. Such events are discarded. In this case, 875 events were removed from the inventory. It should be borne in mind, however, that the disintegration of icebergs located at a similar distance from the hydrophone as the glacier terminus can still be confused with calving events. This issue cannot be addressed in the present study because of the limited view and low temporal resolution of the time-lapse camera and inability to estimate the noise directionality (single-channel recordings). In future studies, two or more hydrophones could be used to identify and discard noise signals not related to the calving activity.

Second, the noise segments are occasionally contaminated with flow noise, which originates from water turbulence advected past the hydrophone and is most pronounced at frequencies below ∼50 Hz. An overlap in frequency between the calving detector band (30–100 Hz) and the flow noise (2–50 Hz) can result in false classifications of the episodes of intense water flow around the hydrophone as calving events. To deal with this issue, we discard all events for which the ratio between the average power spectral density at 2–30 and 50–1000 Hz is higher than or equal to 1. This procedure is based on the observation that calving noise extends into the 50–1000 Hz band, whereas flow noise is most pronounced at frequencies below 30 Hz. Using these criteria, 328 misclassifications were identified and manually validated by listening to the selected noise segments and visual inspections of spectrograms. In total, 1128 events were discarded due to the fact that 75 events were identified as both flow noise and iceberg disintegration.

One issue remains, which is the fact that some fraction of the event signals found come from submarine calving events. Submarine calving events are a problem because the parameters in the power-law relationship between the energy of noise production and kinetic energy of block impact are for subaerial events and will not apply to submarine events (Glowacki and Deane, 2020). Thus any submarine events included in the calving inventory will not have their volume calculated correctly. Moreover, even if their volume were calculated correctly, they are not detected by the camera observations for this study. The analysis of calving flux from submarine events would first require new calibration data (see Sect. A4 in Appendix A for more details).

The total number of submarine calving events in the present inventory is not expected to be large. Reported statistics of submarine calving from other study sites show that such events are typically much less common than subaerial calving (Minowa et al., 2018; Köhler et al., 2019; How et al., 2019). Glowacki (2022) estimated that submarine calving events at Hansbreen are 8–10 times less frequent than subaerial events. It must be noted, however, that the low rate of occurrence of submarine calving is offset by the fact that submarine events often produce the biggest icebergs (Warren et al., 1995; Motyka, 1997; O'Neel et al., 2007; Glowacki, 2022). Consequently, attributing this component of the total calving flux to subaerial events may introduce an error disproportionately large relative to their number. In response to this problem, a new semi-automatic method for distinguishing submarine and subaerial calving events was recently proposed (Glowacki, 2022). However, there is no way at the present time to classify calving styles from sound recordings using fully automated methods. The time and frequency structure of the underwater noise from submarine and subaerial calving differs significantly (Glowacki, 2022); for example, the underwater noise from submarine calving typically has longer duration, with individual sound-source mechanisms separated by the quiescent periods. As a result, a universal calving detector should (i) take into account the differences in time and frequency structure of the calving noise and (ii) be validated with high-frequency time-lapse images synchronized with long-term acoustic recordings; this task is beyond the scope of the present study. Keeping this limitation in mind, the section that follows will explain how the subaerial calving flux can be estimated acoustically, with an assumption that all detected events are subaerial.

Following event detection, the next step is to compute the total noise energy radiated by the calving event at a standard reference distance of 1 m, E_ac,imp. This step requires the calculation of the time- and frequency-integrated energy of the calving noise. The energy of the impact sound radiated by a falling ice block can be expressed in terms of the observed sound energy by accounting for propagation effects and the addition of background noise using the following:

where ρ_w is the water density, c_w is the sound speed, f₀=30 Hz and f₁=100 Hz are lower and upper frequency limits, t₀ is the start time of the calving event determined from the event detector, $\mathrm{\Delta }t=t_{\mathrm{1}}-t_{\mathrm{0}}$ is the calving signal duration, where t₁ is the end time of the calving signal, and TL is the frequency-dependent transmission loss between the hydrophone and the point of ice block impact (in dB). The acoustic signal is integrated over the surface area of a unit sphere (4π) to obtain total noise energy in joules. The two integrals over time, ${\int }_{t_{\mathrm{0}}}^{t_{\mathrm{0}}+\mathrm{\Delta }t}{P}_{xx}\mathrm{d}t$ and ${\int }_{t_{\mathrm{0}}-\mathrm{\Delta }t}^{t_{\mathrm{0}}}{P}_{xx}\mathrm{d}t$, are the frequency spectral densities of the calving noise plus background noise and background noise alone, respectively. The transmission loss is calculated using the standard numerical code RAM (Collins, 1993) (see Appendix A: Materials and methods for further details).

In the next step, the kinetic energy of the falling block of ice, E_imp, is calculated from the total impact sound energy radiated into the bay, E_ac,imp, using the power-law relationship:

where $\mathit{\gamma }=\mathrm{1.45}\times {\mathrm{10}}^{\mathrm{9}}$, κ=0.18 and $\mathit{\zeta }=-\mathrm{2.66}\times {\mathrm{10}}^{\mathrm{9}}$ are constants determined using the calibration dataset collected in 2016 (Glowacki and Deane, 2020; see Appendix A: Materials and methods for details). Finally, the iceberg volume is calculated as

where M is the iceberg mass, ρ_i=917 kg m⁻³ is assumed ice density, g=9.81 m s⁻² is the acceleration due to gravity, and $\widehat{h}=\mathrm{20.7}$ m is the mass-weighted average drop height estimated for the terminus of Hansbreen (Glowacki and Deane, 2020).

Figure 3 shows a comparison of two time series: (i) subaerial calving flux derived from iceberg impact noise and (ii) terminus area loss estimated from camera observations over the 26 d of analysis (see Appendix A: Materials and methods). The ice volume loss was calculated every 3 h, which is the sampling time of the camera system. Both data streams show variability between samples and between each other. This is to be expected; Glowacki and Deane (2020) demonstrated that the acoustic method is accurate if sufficient calving events are averaged but significant variability is observed in the signal between blocks of comparable volume. Moreover, camera observations are sensitive not only to weather conditions but also to the location of calving events due to the irregular shape of the terminus and oblique angle of view (see Fig. 1b). However, there is a clear relationship between the acoustic measurements of subaerial calving fluxes and the time-lapse observation of the terminus area loss, despite the limitations of both methods. The Pearson's correlation coefficient between the two data streams smoothed with a 1 d running average is 0.6. Comparing 2D terminus area loss from images with 3D ice volume loss from acoustic recordings may introduce some artifacts. Nevertheless, the purpose of our approach was to demonstrate the general strong correspondence of calving activity at Hansbreen determined from time-lapse images and underwater noise recordings and thus the overall complementary suitability of this methodology. Computing glacier volume loss due to calving from time-lapse images taken in the study period is problematic for two major reasons: highly oblique camera view and relatively long time intervals between consecutive images (3 h). The latter can easily lead to the classification of several low-magnitude calving events originating in the same sector of the calving front as a single big event. In such a case, the volume loss calculated from the area loss would be largely overestimated; therefore, to better represent the real calving activity, we have decided to stop the image analysis at the calculation of the terminus area loss.

Figure 3A comparison of ice volume loss derived from iceberg impact noise and terminus area loss from camera observations. The ice volume loss was calculated every 3 h, which is the sampling time of the camera system. The thick lines show the two data streams smoothed with 1 d running average.

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The question now is the following: how do the acoustic measurements of the total subaerial calving flux compare to results obtained with more traditional methods? The cumulative subaerial ice volume loss over the 26 d of observation is $\mathrm{1.7}\pm \mathrm{0.7}\times {\mathrm{10}}^{\mathrm{7}}$ m³ from the acoustic measurements and $\mathrm{7}\pm \mathrm{2}\times {\mathrm{10}}^{\mathrm{6}}$ m³ from satellite data combined with stake measurements of the glacier velocity. The discrepancy may be due to several reasons. First, any submarine calving events are treated as subaerial in the acoustic analysis. Consequently, the ice volume loss from acoustics is almost certainly overestimated. This issue has been addressed recently by Glowacki (2022) and can be incorporated into a long-term analysis once a method is developed for the automatic detection of submarine calving. Second, the power-law relationship in Eq. (4) is based on the calibration dataset that does not cover the full range of impact noise energies observed in 2013 data (see Fig. A2 and discussion in Appendix A: Materials and methods). Third, the location of the hydrophone – far from the terminus and in shallow water – was unfavorable because the propagation conditions of the calving noise are very different for different segments of the terminus (see the variable bathymetry along the dashed black lines in Fig. 1a), which has a large effect on the transmission losses of low-frequency sounds in a glacial bay (Glowacki and Deane, 2020). Finally, stake measurements of the ice velocity that were used to calculate subaerial calving flux from satellite images are from August 2013, which is a month before the acoustic data were collected. It is likely that Hansbreen accelerated in September due to heavy rainfall events; such “autumn acceleration” has been reported for other tidewater glaciers in Svalbard (e.g., Luckman et al., 2015; Schellenberger et al., 2015). Moreover, stake measurements do not capture ice velocity variations along the glacier terminus. The results of the experiment presented here are encouraging, given the limitations listed above and completely independent nature of the methods used to make the measurements.

The study of Glowacki and Deane (2020) demonstrated the potential for underwater ambient sound in glacial terminal bays to provide estimates of subaerial calving flux. Guided by this new opportunity, an impact-to-noise conversion model has been applied here to a roughly 1-month long continuous recording of ambient sound in the bay of Hansbreen in Svalbard to estimate subaerial calving flux. Good agreement is found between acoustic measurements of ice volume loss and the camera observations of the terminus area loss. The cumulative subaerial calving flux estimated using the acoustic approach is higher than the ice loss derived using a pair of satellite images combined with stake measurements of the glacier velocity. Clearly, the acoustic method requires further improvements, but the results are encouraging, especially as acoustic recorders are increasingly deployed in the Arctic for other studies, such as studies of biodiversity or human impacts like shipping, and they can be harnessed to also provide measurements of any neighboring glaciers. This study reinforces the idea that passive underwater acoustics offers a new and viable method for monitoring mass loss from marine-terminating glaciers and ice shelves.

The development of algorithms for the automated detection of calving events and the removal of interfering events, such as disintegrating icebergs and flow noise, creates the possibility of monitoring the stability of tidewater glacier termini and ice shelves over long timescales. We envision a scenario where a number of relatively inexpensive autonomous underwater recording systems are deployed over year-long intervals around the termini of selected glaciers on a recurrent schedule. There are many possible selection criteria, but we are interested in (i) glaciers that contribute the most to the sea level rise and stability of major ice sheets and (ii) glaciers that are scientifically important for other reasons (surging, collapsing rapidly, located close to major infrastructure, etc.). The analysis of the resulting signals would eventually allow glacial stability to be monitored over decadal and longer timescales. Concurrent measurements of relevant environmental drivers, such as water temperature, insolation, and precipitation for example, could provide important insights into the processes controlling terminus ablation. Moreover, long-term acoustic monitoring programs could also help to better understand the impact of calving events on ocean stratification, structure and functioning of marine ecosystems, and glacier dynamics itself.

Personal experience making long-term recordings in the Arctic has taught us that not all deployed recording systems are recovered. It is therefore essential to keep the unit cost of recording systems low to allow for as much redundancy as possible within a fixed budget. Power consumption and data storage are two important drivers of cost. Requirements for both of these factors can be reduced by recording ambient sound on a fixed schedule or recording whenever the sound level exceeds a preset threshold. These two possibilities will now be discussed.

Figure 4 shows the effect of recording coverage on the estimated total number of calving events (A) and cumulative ice volume loss (B) over the study period. A continuous acoustic record corresponds to Δ=0 %. Periods of active recording change from 1 h d⁻¹ (≈4 %) to full coverage. Final estimates are derived proportionally; i.e., values obtained for 10 % and 20 % coverage are multiplied by 10 and 5, respectively. The specific hours of recordings during a day are selected repeatedly using all possible combinations, creating a distribution of outputs for the chosen value of coverage. The event count is much less sensitive to the recording schedule than the subaerial calving flux. Nevertheless, 1 standard deviation of the estimated ice volume loss at 30 % coverage is within 10 % of the reference value. This result demonstrates the possibility of significant reduction in recording time (by 70 %) with relatively low increase in the resulting error.

Figure 4The effect of sampling coverage on acoustic estimates of (a) event count and (b) ice volume loss. Recording periods range from 1 h d⁻¹ to continuous. The reference value of Δ=0 % is for full coverage.

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Figure 5 shows the percentage of time occupied by calving noise during the experiment and the acoustic estimate of daily calving rate. On average, calving events were active for only about 1 % of the time; this corresponds to around 120 events per day. However, we expect that the calving detector may split single calving events into several detections. This is especially likely in the case of free falls of highly disintegrated icebergs. Therefore, we assume that the real daily calving rate is likely lower than the acoustic estimate. Although calving activity changes significantly with seasons and geographical location, it is still expected to be a small fraction of the total record. Exploiting this fact through the use of event-driven recording systems could result in significant power savings for autonomous recorders.

Figure 5(blue) Percentage of time occupied by calving noise over the study period and (orange) the acoustic estimate of daily calving rate.

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The acoustic data used in this study are available at https://doi.org/10.34808/jp25-2b47 (Tegowski et al., 2023). Time-lapse images of the Hansbreen's terminus can be downloaded from https://ppdb.us.edu.pl/geonetwork/srv/eng/catalog.search#/metadata/ee0e611b-bfe9-4ba1-95ae-beb0702ae2aa (Ciepły, 2023). CTD data – used for noise propagation modeling – are available at https://dataportal.igf.edu.pl/dataset/inter-calibrated-temperature-and-salinity-in-depth-profiles-in-hornsund-fjord (Moskalik et al., 2022).

JT conceived the project, led the 2013 field expedition to Svalbard and participated in data analysis and interpretation, and participated in manuscript preparation. OG is co-architect of the sound inversion methodology, performed data analysis and interpretation, and participated in manuscript preparation. MC collected and processed the photographic data of terminus ablation. MB collected and processed satellite and stick data of glacier velocity and ice mass loss. JJ provided scientific oversight into data analysis and participated in manuscript preparation. MM participated in the field campaigns and provided CTD data. PB participated in field campaigns and participated in manuscript preparation. GBD is co-architect of the sound inversion methodology and detection algorithm, participated in field campaign, and participated in manuscript preparation.

The contact author has declared that none of the authors has any competing interests.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This research has been supported by the Ministry of Education and Science, Poland (subsidy for the Institute of Geophysics, Polish Academy of Sciences, and grant no. 1621/MOB/V/2017/0), the National Science Centre, Poland (grant nos. 2021/43/D/ST10/00616 and 2011/03/B/ST10/04275), the Centre for Polar Studies, University of Silesia, the U.S. Office of Naval Research, Ocean Acoustics Division (grant no. N00014-17-1-2633), the U.S. National Science Foundation Office of Polar Programs (grant no. OPP-1748265), and Research Council of Norway (Arctic Field Grant, RIS ID: 6133).

This paper was edited by Olaf Eisen and reviewed by Evgeny A. Podolskiy and one anonymous referee.