Glacier calving is a key dynamical process of the Greenland Ice Sheet
and a major driver of its increasing mass loss. Calving waves, generated
by the sudden detachment of ice from the glacier terminus, can reach tens
of meters in height and provide very valuable insights into quantifying calving activity. In this study, we present a new method for the detection of source location, timing, and magnitude of calving waves using a terrestrial radar interferometer. This method was applied to 11 500 1 min interval acquisitions from Eqip Sermia, West Greenland, in July 2018. Over 7 d, more than 2000 calving waves were detected, including waves generated by submarine calving, which are difficult to observe with other methods. Quantitative assessment with a wave power index (WPI) yields a higher wave activity (
Many outlet glaciers of the Greenland Ice Sheet have undergone rapid retreat, thinning, and flow acceleration within the past 2 decades
Glacier calving, a sudden fracture phenomenon that releases large quantities of ice to the proglacial fjord during short-lived events, has been identified as an important factor in the dynamics of tidewater glaciers
Glacier calving events generate ocean waves by falling ice chunks, rotational detachment of full-thickness ice blocks, or buoyant up-rise of submerged ice. Such calving waves can reach heights exceeding 50 m and create damaging tsunami waves upon run-up on the shores
Studying the origin, mechanism, source impact, and spreading of surface calving waves in space and time remains a challenge due to their transient characteristics, a variety of source mechanisms, and the heterogeneous and dynamic propagation environment in iceberg-covered fjords. Here, we present a method to investigate calving event source positions by back-tracking wave trains captured with a terrestrial radar interferometer (TRI). To our knowledge, this is the first application of a TRI to observe and quantify surface calving waves. The method was successfully applied to the detection of more than 2000 calving events within a data set acquired over 7 d at Eqip Sermia, West Greenland. In the following, we first present the study site and data before describing the different steps of the method. We proceed to analyze the associated results and discuss the challenges linked to calving wave detection and method improvements. Finally, we extend our analysis by combining our results of calving wave activity with a detection of visible meltwater plume occurrences.
Eqip Sermia (69.80
Eqip Sermia in West Greenland flows into a shallow fjord. Clearly visible are freshly calved icebergs and drifting ice debris pushed out by the brownish meltwater plume (under the letter S). The positions of the terrestrial radar interferometer (TRI) and the pressure sensor (PS) are indicated by orange and yellow triangles. Sectors ending in shallow (S) and deep (D) waters are separated by a black dashed line at the calving front. Background: Sentinel-2A scene from 19 July 2018 (Copernicus Sentinel data 2018, processed by ESA).
A terrestrial radar interferometer
A pressure sensor was installed on the shore in front of the TRI to record the water pressure in the fjord (3.5 km away from the calving front; position PS in Fig.
Example of calving wave detection.
Steps of the wave detection algorithm TeRACWA (Terrestrial Radar Assessment of Calving Wave Activity). Steps linked by dashed and solid arrows are respectively applied to each TRI acquisition and to the resulting data set.
The TRI registered in a 1 min interval the signal strength and phase of reflecting natural surfaces on the glacier and the fjord, such as ice faces, rocks, and icebergs. The raw radar acquisitions were stored as complex numbers in
Figure
Determination of the frequency high cutoff by analyzing the power spectra of
We developed a novel algorithm to automatically detect calving waves, their origin, and a measure of their magnitude in time series of radar acquisitions named TeRACWA (Terrestrial Radar Assessment of Calving Wave Activity). The algorithm was implemented in the Python programming language, using the SciPy and multiprocessing libraries for signal processing and parallel algorithm execution
The following processing steps 3–6 were applied to each resulting differenced image. More specifically, step 3 was applied to the signal
strength of each individual azimuth line of each differenced image, further referred to as the one-dimensional array.
The low-cutoff wavelength was selected by analyzing the power spectrum of 60 different signals, each of which is the average of four neighboring azimuth lines. Half of these signals were taken from acquisitions containing calving waves with azimuth lines around the source locations (Fig.
The final product consists of a catalog of wave generation times and along-front locations, as well as associated wave magnitudes quantified by an empirical wave power index (WPI) throughout the field season. From this catalog, spatially and temporally cumulated and averaged WPI values were computed. The spatially cumulated WPI consisted of the sum of WPI values along the calving front at a given time step, further applied to all time steps. The temporally cumulated WPI consisted of the sum of WPI values through time for a given azimuth line (image horizontal row), further applied to all azimuth lines.
The water pressure sensor data show that the fjord was very calm without the forcing from calving events. Background waves driven by winds or ocean swells were mostly absent. For each calving event the water height data show direct and reflected waves of many amplitudes. To obtain a quantitative relation between the WPI detected by TeRACWA and wave amplitudes measured with the pressure sensor, we calculated a quantity called “integrated wave height squared” (IWHS) as a measure of wave energy reaching the shore. Simpler measures, such as maximum wave height, proved to be less suitable as they do not capture the temporal evolution of the wave signal. The IWHS was computed during an interval of
The integration interval
Results of the automatic wave detection by TeRACWA during the 2018 field season.
With the aim of studying the relation between meltwater plume occurrence and calving wave activity, we manually quantified visible meltwater plumes. Plume footprints are clearly discernible on optical imagery as growing sediment-rich, brownish areas close to the water surface, and whether the fjord is ice covered or not (Figs.
The TeRACWA algorithm was applied to co-registered TRI data from the 2018 field season from 7 to 15 July. Within the 11 479 acquisitions in 1 min intervals over 7.49 d, a total of 2418 calving waves were automatically detected, resulting in an average of 13.4 calving waves per hour. Figure
Both the spatial variability and temporal variability of calving wave activity are large, with episodic quiet and active phases along different parts of the calving front. Due to the distinctly different characteristics in ice cliff geometry and water depth, the calving front can be divided into sectors with shallow and deep water, which exhibit different calving behavior and event size statistics
The results in Fig.
Figure
To further quantify statistical characteristics of the observed wave activity, recurrence times
Wave recurrence time for a range of WPI values. The orange line corresponds to a power law fit using non-linear least squares, where
Figure
The results presented above suggest a strong correlation between the spatially distributed wave heights from which the WPI is calculated and the point measurement of water level variations at the shore from which the “wave energy” is quantified with the IWHS. However, it is important to note that the low number of points associated with the uneven distribution of values results in a heterogeneous point weight in the linear regression. The latter is therefore significantly affected by isolated values (e.g., by the highest WPI value). A larger data set would be required to strengthen this relation.
Figure
Temporally cumulated wave power index (orange bars; identical to Fig.
We presented a novel method (TeRACWA) for the detection and the quantitative assessment of calving activity by analysis of calving waves recorded with a TRI. This method is complementary to other methods such as calving volume estimates by subtraction of digital elevation models (DEMs) derived from drone imagery or from TRI interferometry
Each of these methods detects different aspects of the calving process. High-rate TRI interferometry provides detailed calving volumes and the locations of sources above the water line, but submarine calving events currently escape detection largely because of the loss of signal coherence over the ocean surface. Analysis of high-rate time-lapse photography provides dense coverage of events but is difficult to quantify and can be challenging to automate. Calving waves at remote shores provide estimates of the calving impact on the ocean but are difficult to interpret in terms of ice volume and source location due to various calving styles and wave propagation phenomena. Passive seismology captures mainly large events with distinct fracturing and ice-rotational processes
Our novel TeRACWA method detects calving waves from all calving styles and reliably provides source location and timing. The method detects secondary effects of the calving process and therefore yields information not available from other methods. At present, however, the method cannot discern between different calving styles. A combination of several methods would be a promising avenue to a clearer understanding of the whole calving process including fracture, ice failure, ocean impact, and wave propagation.
In this section, we discuss challenges associated with the method validation and specifically the comparison of TeRACWA results with the pressure sensor measurements and with another TRI-based calving event detection method. Finally, a possible validation setup is proposed.
A comparison of the WPI determined by TeRACWA with wave amplitudes derived from pressure measurements was presented in Sect.
The two TRI-based calving detection methods TeRACWA and the surface elevation change extraction method (SECEM)
The first requirement is that both methods capture the same calving events. This is certainly fulfilled for big subaerial changes in ice volume, as each large chunk of ice falling into the fjord creates a wave detected by TeRACWA with a height linked at the first order to the ice volume. However, there is no direct per-event proportionality between falling ice volume and the height of the resulting wave, which depends on the elevation above water of the detached ice mass and details like impact angle, fragment size, and water depth. The local terminus geometry such as the front slope and the presence or absence of bedrock above the water line before any contact with the ocean surface are also important parameters affecting the wave properties. Furthermore, not all detected waves stem from changes in subaerial ice volume. Submarine calving events can only be detected by their wave action through TeRACWA without a counterpart in the SECEM results.
The second requirement is that events of all sizes are detected by both methods. Both methods feature a lower detection limit to prevent false detection of noise. These thresholds, 5 m in height for SECEM DEM differentiation and 4.5 in WPI for TeRACWA, are based on different quantities and are therefore not suppressing the same events.
Finally, it is important to note that SECEM involves a temporal stacking of 10 min in order to reduce noise from atmospheric disturbances. Events within each stacked period are therefore merged together, requiring resampling of the TeRACWA results for a meaningful comparison.
Despite these method differences, we find similarities in the results from TeRACWA and SECEM
One possible approach to robustly validate the wave detection algorithm in space and time as well as the inferred wave power would be the installation of a pressure sensor or a GNSS Wave Glider
Directly detecting calving waves is challenging for a number of reasons. Calving waves are a transient phenomenon and leave no trace after their dissipation, thus preventing temporal stacking of radar acquisitions for noise reduction. A small sampling interval and low atmospheric disturbances are thus mandatory for sufficiently high-quality data. Due to wave speeds exceeding 30 m s
The main limitation of the proposed method is linked to the heterogeneous properties of the proglacial marine environment, both spatially and temporally. The radar signal scatter intensity strongly depends on position, size, and shape of natural reflectors. Icebergs and small pieces of floating ice debris are continually shifting, driven by wind, tides, and subglacial meltwater plumes. Consequently, the recorded scattering intensity of a calving wave propagating along a rough ice-covered fjord surface will be significantly higher than that of an ice-free and smooth water surface. In the study case presented here, cold conditions with a high ice cover during the acquisition period alleviated this limitation, which nevertheless has to be carefully taken into account for warmer years like 2019. Signal normalization (TeRACWA step 4) compensates for the effects of variations in radar intensity caused by varying ice cover of the fjord. In addition, differencing of the raw signal of consecutive acquisitions (TeRACWA step 2) significantly reduces the imprint of stable or slow-moving ice mélange and icebergs, albeit not from highly dynamic areas like the meltwater plume. While these problems reduce the accuracy of the derived wave intensity (WPI), they do not affect the wave detection itself in the case of high wave amplitudes. For low wave amplitudes resulting in WPI values close to the WPI threshold, the ice cover can be determinant in the classification of a signal as wave or background noise. Nevertheless, the WPI threshold is set automatically based on the study of the data set distribution. We therefore suggest the automatic adjustment of the threshold depending on the data set to reduce the influence of this limitation. Applications of TeRACWA for different ice cover conditions in future work will however be needed to further assess this influence. An accurate temporal and spatial tracking of the ice cover motion could improve the normalization of the radar intensity and the WPI determination. Unfortunately, none of the many tested methods provided good results and high efficiency, such that we decided to use the simple corrections of algorithm steps 2 and 4. For our application of TeRACWA in summer 2018 the strongly ice-covered Eqip Sermia bay largely alleviated these limitations.
A further potential error is due to the portion of the pixel mask upstream of the average calving front and extending onto the glacier. There, crevasses scatter the radar signal and contribute to the WPI. The differencing of consecutive acquisitions (TeRACWA step 2) and the quantification of the background signal (TeRACWA step 3) reduce the recorded signal from these uninteresting scatterers. Nevertheless, changes of the glacier geometry, such as from ice motion and calving, affect the signal used for wave detection. Ideally, the ocean–glacier interface could be detected at high temporal and spatial resolution and therefore alleviate the need of the buffer zone on the ice. For this purpose, an automatic calving front detection algorithm was developed based on the analysis of abrupt signal strength changes from fjord water to ice. However, a temporal stacking over several hours was needed to retrieve a clear signal without the influence of icebergs and ice-covered areas. Using a delineation of the glacier terminus at such low time resolution would result in an abrupt and unreal evolution of the ROI when switching from a stacked period to the next, strongly affecting the consistency of TeRACWA results over time. Consequently, the simple and static extraction of the glacier terminus (TeRACWA step 0) was used.
The method accuracy is questionable in the case of multiple large calving events in rapid succession in a restricted area (within several minutes and few hundred of meters), an uncommon but possible situation. Such event sequences induce wave superposition and create complex wave patterns that are difficult to disentangle. For such cases, our method (based on a one-dimensional Fourier transform) often struggles to distinguish the different waves due to lack of spatial information. Trials with 2D Fourier transforms showed no clear results, likely due to the inconsistency between the dimensions of the radar images at different spatial resolution, and with azimuth lines acquired sequentially at different times.
The TRI viewing angle with respect to the calving front is a potential source of uncertainty. As waves propagate in circles, and the Fourier transform amplitude is maximum at their center, results are not sensitive to small variations in calving front orientation. However, in portions of the glacier front with extreme orientations (e.g., approximate azimuth angle of 24
Following a careful assessment of the different limitations presented in this section as well as a possible adjustment of the cutoff wavelengths, the proposed method could be applied to other outlet glaciers with various calving styles. This would allow for a better understanding of the factors affecting the results and consequently render the method more robust. Ultimately, the method should become applicable to glaciers with various front geometries, bathymetries, and ocean ice cover.
In this section we discuss and interpret the spatial and temporal evolution of the observed calving wave activity. Special emphasis is given to the influence of meltwater plumes on the calving process and calving activity.
A long-term increase in spatially cumulated WPI was observed (time correlation of 0.68) during the 2018 field season. However, we found no direct relation with air temperature, humidity, or shortwave radiation, suggesting no direct meteorological influence. Also, no evidence for an influence of tides on calving was found during the 7 d period. These conclusions support earlier findings
A marked spatial variation in calving wave activity was observed along the glacier front. In the deep sector the average temporally cumulated WPI was
34 % higher at a 26 % smaller width compared to the shallow sector.
Normalized by sector width, this difference amounts to 49 %, illustrating two distinct calving regimes (Fig.
Subglacial discharge of meltwater into the ocean forms rising plumes and increases submarine melting by entraining warmer ocean bottom water to the calving front. Such submarine melting has been identified as an enhancing mechanism for calving and potential glacier destabilization
Comparing the temporally cumulated WPI with the presence of meltwater plumes yields a clear relationship. Figure
The strong correlation between meltwater plumes and calving activity, especially in the deep sector, can be explained by the occurrence of large submarine plumes and resulting melt undercutting. Along a deep submerged calving front more warm and salty deep water is entrained in meltwater plumes and rises along a larger exposed area of calving front
From these observations we conclude that an important part of the higher calving activity in the deep sector is explained by a combination of a higher occurrence of meltwater plumes and a more efficient heat exchange with warm rising waters. These conclusions could be improved by determining the change rate of the plume footprint area on the fjord surface, which gives an estimate of water flux within the meltwater plume. To this end an automated detection algorithm is needed with high temporal and spatial resolution. Our attempts to develop such a method based on watershed algorithms were unsatisfactory due to an insufficient detection accuracy. The main limitation was the difficulty to accurately detect the calving front on single radar acquisitions (see Sect. 5.2). While the automatic tracking of growing meltwater plume extent at known locations was successful, the detection of newly formed plume footprints was complicated by low-backscatter features on the glacier such as crevasses.
The above discussions and interpretations are based on unique high-resolution observations during a 7 d period. Such a short time period captures only a short-lived snapshot of the very dynamic processes at the calving front during the melt season. Our observations only capture a limited range of environmental conditions and processes, and more processes and changing dynamics might be active throughout the melt season. Likely larger differences in calving regimes can be observed throughout the summer, or between years. Longer and more frequent continuous field observations are therefore crucial to study calving processes in a variety of hydro-meteorological and environmental contexts. Our understanding of the complex calving phenomenon and its various implications hinges on precise high-resolution observations with many complementary methods.
We developed a novel automated method named TeRACWA (Terrestrial Radar Assessment of Calving Wave Activity) for the detection and the quantification of ocean waves generated by glacier calving. Using radar scatter intensity from a terrestrial radar interferometer (TRI), the algorithm yields timing and source location of calving events, as well as a measure of wave power quantified by a unit-less wave power index (WPI). It offers the new possibility to detect submarine calving events, a calving style imperceptible with other TRI algorithms. This method was successfully applied to
The recognition of calving events from wave patterns is complementary to other calving detection approaches such as source identification from time-lapse photography, volume estimates from DEM differentiation, or analysis of seismic signals. By using complementary information on various aspects of the calving process from different methods, this crucial process can be studied in more detail. In addition to the new possibility to detect submarine calving events, our method can be applied for re-analysis of existing TRI data sets.
The calving process is a complex phenomenon that can only be investigated in depth by combining different complementary observation approaches. In this way, process understanding from the analysis of high-resolution in situ measurements constitutes a major tool to constrain detailed numerical calving models. Ultimately, this will yield a better understanding of calving dynamics, which is crucial in high-resolution ice sheet modeling for assessing the future evolution of the major ice sheets.
Timing of the three highest wave power indexes (orange bars;
The implementation of the TeRACWA method is presented in a Zenodo repository:
Animation of consecutive 1 min interval radar images from 9 July 2018 at 13:00:00 to 22:00:00 UTC represented as the logarithm of the signal strength (
AWe drafted the manuscript and performed the data analysis. AWe, ML, AV, and AWa performed the field measurements. GJ performed and analyzed the drone flights. All authors contributed to the editing and reviewing of the manuscript. All authors have read and agreed to the published version of the paper.
The contact author has declared that neither they nor their co-authors have any competing interests.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
We thank Diego Wasser, Eef van Dongen, and the UZH Field Excursion students for their help during the field campaign at Eqip Sermia.
This research has been supported by the Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (grant nos. 200021_156098 and 200020_197015) and the University of Zurich (Forschungskredit FK-19-090) (Andrea Walter).
This paper was edited by Benjamin Smith and reviewed by Surui Xie and Ryan Cassotto.