Unlike the large majority of land-terminating glaciers, marine and lake-terminating (MALT) glaciers reach a water body at a low elevation. The contact surface is often referred to as the calving front. Their ice is lost by sub-marine melting or calving, i.e., ice that breaks off, gets de-connected, and starts to float freely in the form of icebergs or ice floes. Both processes, sub-marine melting and calving, determine the total frontal ablation, i.e., the mass loss at the calving front. Frontal ablation is often a dominant factor in the total mass budget of MALT glaciers . Besides its importance in the total glacier mass balance, the representation of processes controlling frontal ablation is currently a pressing task for numerical glacier models . Neglecting frontal ablation can introduce an important bias. analyzed the impact on ice thickness reconstruction (based on mass conservation) in Alaska and reported an underestimation of 19 % on regional scales and up to 30 % on glacier scales. Various successful approaches exist to parameterize frontal ablation for individual glaciers. Still, the implementation in large-scale or global models is limited by the amount and quality of measurements for constraining the models . Thus, large-scale measurements (ideally time series) of frontal ablation are demanded by the modeling community . Driving forces of frontal ablation are, on the one hand, ice flux (higher flux, e.g., due to bed lubrication by meltwater, can trigger calving events) and, on the other hand, marine factors such as ocean temperature, fjord bathymetry, and sea ice or ice mélange conditions . For example, the persistence of the ice mélange in front of the glacier can stabilize the calving front and affect the glacier dynamics. In contrast, the breakup of the ice mélange can lead to increased calving and ice flow at the glacier terminus . Moreover, a significant frontal retreat can also indicate a retreat of the grounding zone . The retreat of the grounding zone of a glacier with retrograde bedrock formation will lead to further grounding-zone retreat, resulting in increased ice loss and destabilization of the glacier or ice stream . Thus, information on the temporal variability of the calving-front position provides fundamental information on the state of the glacier or ice stream. Therefore, the glacier area has been defined as an essential climate variable (ECV) product by the World Meteorological Organization (WMO). Calving-front positions were usually manually mapped using different remote sensing imagery . Only a few studies applied automatic or semi-automatic approaches. In polar regions, the ocean downstream of the glaciers is often covered by sea ice and calved-off icebergs, forming the so-called ice mélange, making calving-front delineation a challenging task, even when captured by hand. Deep learning approaches have shown high potential for carrying out such complex segmentation tasks, e.g., on medical imagery . In recent years, the application of deep learning techniques for glacier front detection started . Calving fronts can be located in both optical and synthetic aperture radar (SAR) imagery. In optical imagery, calving fronts are more easily distinguishable, whereas synthetic aperture radar imagery has a higher scene availability as this is independent of daytime, season, and cloud coverage . A direct comparison between the results of existing deep-learning-based calving-front extraction studies is not possible as the models have been trained on different data, tested on different test sets, and evaluated using slightly differing metrics.

The benchmark dataset published by provides 681 SAR images of calving fronts. SAR imagery is independent of sunlight and cloud coverage, enabling continuous temporal coverage of the observation area, but compared to optical data, it has only one channel and has more speckle noise. For every SAR image, two labels are provided. One label provides four classes: ocean, glacier, rock, and no information available (e.g., radar shadow and layover areas, areas outside the swath). The other label marks the calving front with a one-pixel-wide line. Based on the training set of the dataset, train a modified U-Net for each label. One U-Net solves the task of glacier segmentation, and one detects the calving front. On the two test glaciers of the dataset, the segmentation model achieves an IoU (Intersection over Union) of 67.7±0.6. By taking the boundary between ocean and glacier, they extract a prediction of the calving front from the zone prediction with a mean distance error (MDE) of 753±76 m. The model trained directly on the front label achieved an MDE of 887±189 m.

In this work, we present a method that utilizes both labels of the dataset instead of training separate models for each task (see Fig. ). Multi-task learning (MTL) is a technique for machine learning algorithms that uses one model to tackle multiple tasks. In most cases, the potentially larger dataset and higher information content lead to higher performance for the individual tasks .

Our method is based on the nnU-Net (no new U-Net) proposed by , which is an out-of-the-box framework for training the U-Net. The framework contains proven deep learning techniques and established hyperparameter values, as well as rule-based parameters that depend on the properties of the dataset and available GPU memory. Therefore, the nnU-Net is a powerful tool that simplifies the application of deep learning algorithms. Its performance in the segmentation of SAR data has not been tested, and the availability of two labels suggests the modification of the nnU-Net for MTL. As a baseline for our evaluation of the nnU-Net, we use the results of .

In particular, our contributions are as follows: (1) visualizations showing the temporal and spatial distribution of the dataset by ; (2) application and evaluation of the nnU-Net for calving-front detection and zone segmentation; (3) two different modifications of the original nnU-Net to incorporate both labels for multi-task learning; (4) testing if an artificial third label improves the calving-front detection; (5) introduction of an efficient approach that fuses the two labels of the dataset; and (6) analysis of the influence of season, glacier, and satellite on the performance of the model.

The paper is organized as follows: after presenting the related work in Sect. , we give an overview of the dataset in Sect. . Section  explains the method and our six experimental setups. Section  examines the results and analyses the influence of different properties of the satellite images. Section  summarises the work.

Automated monitoring of glacier-covered areas is a growing research field. Recent glacier monitoring uses deep learning methods due to the increasing availability of satellite images and computing power. Many methods are based on the U-Net . They modify the vanilla U-Net for better performance in calving-front detection . One approach is to segment the images into different areas and extract the calving front as the border between segmentation areas . Another approach directly trains a model on the position of the calving front . This task suffers from severe class imbalance due to the thin calving front. Researchers approach this problem by creating a distance map from every pixel to the front line. The network is trained on the distance map instead of the thin front line. The actual front-line prediction is then extracted during post-processing.

Other works use the segmentation network DeepLabv3  to detect calving fronts. The main advantage of DeepLabv3 over U-Net is the atrous spatial pyramid pooling, which makes the network adaptable to different image resolutions .

The Calving Front Machine (CALFIN) proposed by segments optical and SAR images into the ocean–land zones and extracts the calving front during post-processing with a topography map of the area. Researchers apply MTL with a late-branching architecture. They use two labels: a binary ocean mask and a binary calving-front mask. They achieve state-of-the-art predictions with an 86 m deviation from the measured calving front. A detailed comparison to the aforementioned U-Net-based methods by and  revealed the generalization ability of CALFIN to other glacier datasets. The images had to be down-sampled for CALFIN. Therefore, the distance in meters doubles, but comparing the pixel distance errors reveals a similar performance. With 29 million parameters, CALFIN is still a large network that needs a large amount of training data. propose a similar approach for medical image segmentation and show that the individual tasks benefit from MTL. Several other approaches have advanced the U-Net architecture for MTL for medical applications . The work of uses MTL for the segmentation of a binary ocean–land mask and for edge detection of the Antarctic coastline, where the calving front is just part of the coastline. They add task-specific heads for the two tasks to the U-Net. They achieve results with a deviation from the reference of 345 m compared to 483 m with the vanilla U-Net. To avoid distortions of the metric from areas far from the coast, the metric is calculated within 2 km of the true coastline. A further development of the holistically nested edge detection (HED)-UNet for Antarctic ice shelf front detection is proposed by . Their post-processing includes an elevation threshold of 110 m to remove erroneous classifications in the high-altitude dry-snow zones.

The dataset used in this work is provided by . It contains 681 synthetic aperture radar (SAR) images of seven marine-terminating glaciers taken by six different satellites. Two glaciers are located in the Northern Hemisphere, namely Columbia Glacier in Alaska and Jacobshavn Isbrae (Sermeq Kujalleq) (JAK) in Greenland. The five glaciers in the Southern Hemisphere are all located on the Antarctic Peninsula (see Fig. ). The Crane, Mapple, and Jorum glaciers are closest to the south pole, followed by Dinsmoore–Bombardier–Edgeworth (DBE). They are located so close together that they are treated as one glacier site. The last glacier is the Sjögren-Inlet Glacier.

Table  lists the seven glacier sites with the number of images and the area they show. The table also depicts the train–test split. The samples of the training set are used for the parameter optimization of the segmentation method, and the test set is exclusively used for evaluating the method. The test set contains the glaciers Mapple and Columbia. Columbia is the only mountain glacier in the dataset. The other glaciers are outlet glaciers of polar ice sheets. Therefore, Columbia can be seen as a benchmark glacier for the generalization capability of the segmentation method. Columbia and Mapple also differ in terms of the shape of the glacier. The images of Columbia show multiple calving fronts in one image, and the flow of the glacier arms goes in different directions. On the other hand, Mapple is a less complex glacier, moving in only one direction with one clearly defined calving front between the lateral fjord side walls.

The dataset contains two labels and a bounding box of the glacier for each SAR image. One shows a mask of the different zones of the glacier (ocean, glacier, no information available, rock). The other label contains a one-pixel-wide line representing the calving front. The bounding box is not utilized for our method. A sample of each glacier in the training set with its corresponding labels is shown in Fig. . Predicting the zone mask can be seen as a classic segmentation problem. The calving front can also be extracted from the zone label by taking the border between ocean and ice areas in the corresponding bounding box. The direct delineation of the calving front is a more difficult task due to the high-class imbalance. Fewer than 1 % of the pixels are labeled as front pixels. Additionally, the structure of the class region is not a convex hull but a thin line.

Corresponding to the change in glacier area, the position of the calving front changes. In Fig. , the retreat of Columbia is visualized by plotting the calving-front position of every sample in a different color. The bright lines represent past calving fronts, and the dark-red lines represent the more recent positions. The constant retreat of Columbia is visible through the tiered lines. The visualization of the glaciers in the Southern Hemisphere is included in Appendix . The change in the class distribution of the zone labels over time is shown in Appendix .

Every glacier is captured by multiple satellites for a higher temporal resolution and extended observation periods, meaning that recordings of one glacier are captured by different SAR systems with different image resolutions. The resolution refers to the ground range resolution. The Environmental Satellite (ENVISAT), European Remote Sensing Satellite 2 (ERS-2), and Sentinel-1 (S1) have a resolution of 20 m, the phased-array-type L-band SAR (PALSAR) has a 17 m resolution, and TanDEM-X (TDX) has a 7 m per pixel resolution. Unfortunately, the dataset does not provide information about the polarization. In Fig. , a timeline of the images of each glacier visualizes the observation time and frequency of the images. The first two rows show the glaciers of the test set.

In this section, we explain our method, which includes the utilization of the nnU-Net as a framework that simplifies the training of a U-Net. We document our six experimental setups that aim to evaluate the impact of multi-task learning (MTL) on the training of the U-Net.

In this section, we will examine our evaluation metrics, compare the results of the six proposed experiments, and evaluate the results of the fused-label experiment. We used a 5-fold cross-validation for the evaluation to eliminate the weight initialization bias and the bias caused by a single split into training and validation sets. The metric scores of the individual models are averaged to get a robust measure independent of weight initialization and split.

This work explores the use of the nnU-Net by in segmenting glacier-calving fronts. The nnU-Net promises an out-of-the-box application of deep learning for segmentation tasks. We evaluate this claim using a dataset of glacier images provided by . The dataset contains two tasks: the calving-front detection and the glacier zone segmentation. We try different modifications of multi-task learning (MTL) with two different neural-network architectures to tackle both tasks simultaneously. The results show that combining both tasks increases each task's performance. No significant difference between the two MTL architectures exists. Adding more domain-specific tasks like glacier boundary delineation does not further improve the previous tasks. Due to the small area of the front line, the two labels can be fused into one label. The fusion of labels decreases the number of parameters used, shortens the training time, and reduces the deep learning expertise needed as the nnU-Net can be used without modifications. This approach achieves an average MDE of 541±84 m. We provide the code and the pre-trained model for application on further SAR images of glacier fronts (see “Code and data availability” section). The predictions need to be filtered manually since there can be outliers, as our results show. However, this will provide an initial prediction, which eases the task of glacier front delineation.

To improve the average MDE, future work should focus on reducing the model performance with low-resolution images, such as with Sentinel-1 with 20 m per pixel resolution. This can be done by including more images taken by Sentinel-1 in the training set or by implementing an oversampling strategy of the low-resolution images.

The framework nnU-Net is well suited to segmenting SAR images of glaciers and calving-front delineation. The modification of the nnU-Net for MTL improves the results compared to STL experiments, where only one label is used. However, it is not necessary for glacier segmentation and calving-front delineation because both labels can be fused without losing a significant amount of information. Our findings highlight the suitability of the nnU-net for glacier front segmentation with multi-mission SAR remote sensing data, which will facilitate an efficient, extended spatiotemporal mapping of tidewater glacier terminus changes. Our findings also promote the out-of-the-box application of the nnU-Net for other segmentation tasks based on satellite imagery because we did not need to modify it for the calving-front detection.