Permafrost constitutes subsurface materials that remain continuously at or below 0 ∘C for at least 2 consecutive years. The rapidly increasing temperatures recorded since the 1980s have initiated permafrost degradation in many Arctic regions (Smith et al., 2022; Biskaborn et al., 2019). The cryosphere (including sea ice, glaciers, lake and river ice, continental ice sheets, seasonal snow, permafrost, and seasonally frozen ground) covers 14 % of the Earth's surface. Some atmospheric hazards such as hail, frost, and freezing rain have globally decreased in recent years (Ding et al., 2021). In Arctic conditions, this effect implies a reduced ice cover forming over the underlying permafrost soil, which therefore in turn gets increasingly exposed to subaerial conditions (Gilbert et al., 2018). This mechanism is, together with prolonged seasons with +0∘C, one of the main drivers of permafrost degradation. Permanent thawing of the internal ice in permafrost soils often leads to subsidence and slumps, which are called thermokarst (Kokelj and Jorgenson, 2013).

Thermokarst is a significant threat in Arctic environments, and numerous examples of its negative effects have been reported at various scales, across several ecosystems (Voigt et al., 2019), for different infrastructure types (Hjort et al., 2018, 2022), and at cultural heritage sites (Nicu et al., 2021a, b, 2022c). Aside from these directly observable effects on the ground, permafrost thawing can also release greenhouse gases such as carbon dioxide and methane into the atmosphere, thus contributing to global warming (Oberle et al., 2019; Ran et al., 2022). At the mesoscale, one of the consequences of warming permafrost ground consists of the deepening of the active layer. This layer represents the uppermost part of the soil column, subjected to seasonal thawing and refreezing. Therefore, as warming occurs, the part of the soil column where this cycle takes place becomes increasingly deep, whereas previously ice would have held the soil particles together at these depths (Frey and Mcclelland, 2009; Schaefer et al., 2011). In turn, this naturally results in reduced cohesion between soil particles, something that can promote the initiation of geomorphic processes unique to Arctic environments, known as thaw slumps (TSs; also depending on water released from ground ice) (Cassidy et al., 2017) and thermo-erosion gullies (TEGs) (Godin et al., 2012). The precise feedback mechanisms involved in TS and TEG activity are still relatively poorly understood.

A TS is caused by the thawing of ice-rich permafrost which, independently or together with precipitation, results in oversaturated soils. This induces a significant loss in terms of shear strength and may lead to soil collapses, forming slumps (Daanen et al., 2012). TSs can initiate along an erosive riverbank or shoreline or even within a TEG, where fluvial erosion exposes ice-rich frozen ground to rapid thawing (Nicu et al., 2021a; Cassidy et al., 2017). Conversely, a TEG may be initiated in response to heat transfer along preferential directions. This is the case when water infiltrates into the soil column warming the surrounding material and causing loss of cohesion. This may occur in or along seasonal freeze cracks in the ground, sometimes in connection to ice-wedge polygons. Something that can also add further instability is the increase in the active layer's depth due to the same heat transfer process. Below the active layer, the ground remains permanently frozen, with the upper portion commonly referred to as the transition zone (Godin et al., 2012). This ice-rich transition zone will, if thawed, release excess water that may further initiate small-scale fluvial processes and small slumps or grain collapses. TEGs can develop both retrogressively upslope and through widening/deepening of the initial incision (Iwahana et al., 2014; Nicu et al., 2022c).

Over the last few years, there has been an increasing interest in studies referring to TS activity in permafrost regions of China (Niu et al., 2015; Xia et al., 2022), Russia (Séjourné et al., 2015), Alaska (Swanson and Nolan, 2018; Swanson, 2021), Canada (Lewkowicz and Way, 2019), and Svalbard (Nicu et al., 2021a). TEGs are less studied, except for a few cases in Canada (Godin et al., 2014, 2019), Russia (Sidorchuk, 2019), and Svalbard (Nicu et al., 2022c). Hardly any of these research efforts though have focused on learning from past TS and TEG occurrences to estimate locations where they may form in the future (Yin et al., 2021). This concept, at lower latitudes and for other geomorphological processes, is usually referred to as susceptibility or the probability of a given process occurring across a given landscape (Hansen, 1984). However, single susceptibility maps would not be highly informative in an Arctic context where TSs and TEGs can take place within the same terrain and be mutually triggering. For this reason, a much more interesting scientific product would consist of a multi-hazard susceptibility map where the likelihood of TSs and TEGs is combined to highlight locations where these processes may contextually initiate and develop.

Multi-hazard assessment is also part of Agenda 21 for Sustainable Development (UN Department of Economic and Social Affairs, 1992). Its relevance is highlighted in the context of risk reduction strategies because the combination of one or more hazards together (especially cryospheric ones) may be more threatening than the occurrence of one (Kappes et al., 2012). Even aside from the specific peri-Arctic context, multi-hazard susceptibility modelling is rarely touched upon, with few examples of landslides and gully erosion (Lombardo et al., 2020), rockfall and debris fall (Saha et al., 2021), and floods, landslides, and gully erosion (Javidan et al., 2021). Specifically in the context of cryospheric hazards though, the current literature offers no examples in the Arctic.

Our work fits in this gap and aims to bring two essential elements to the attention of the geoscientific community. The first is related to the limited availability of cryospheric hazard inventories, for which we try here to promote a positive habit of data sharing, a fundamental aspect of scientific progress especially when working in an unchartered territory such as the Arctic regions, local processes, and their manifestation in response to climate change. For this reason, we share the first update of two TS and TEG inventories mapped across Nordenskiöld Land (Svalbard Archipelago), an area covering about 4000 km2. The second objective of this work is to produce locally valuable probabilistic estimates of TS and TEG occurrences and their multi-hazard relation. This is achieved by implementing two separate binomial generalised additive models (GAMs), whose results are explored in depth both by interpreting landscape characteristics associated with one or the other hazard under consideration and by validating the predictive patterns via a set of performance assessment tools.

Svalbard Archipelago covers an area of about 61 020 km2 and is located halfway between the North Pole and the coast of Norway (Fig. 1a) (Zwoliński et al., 2013). The study area is in central Spitsbergen (Fig. 1b), which represents the largest island of the Svalbard Archipelago (governed by Norway and established by the Spitsbergen Treaty on 9 February 1920). The average annual air temperature for Svalbard calculated for the 30 years between 1988 and 2017 was 1.5 ∘C higher than the same for the reference period 1971–2000 (Hanssen-Bauer et al., 2019). In Svalbard, the projected temperature increase in the 21st century varies from a few percent in the south-west to more than 40 % in the north-east (Førland et al., 2011). This increase in temperature is likely to be driven by sea ice decline, higher sea surface temperature, and a general background warming (Isaksen et al., 2016). As a result, the permafrost is expected to degrade even further in the future. Moreover, a significant increase in rainfall discharges has been locally recorded over the last century, with annual precipitation in 1940 measured at 482 mm and reaching 704 mm in 2018. The period between October and March corresponds to the wettest season (overlapping the period of high cyclonic activity), followed from April to July by the driest. Specifically, precipitation during winter is up to 2 times higher than in summertime (Demidov et al., 2021).

Svalbard represents one of the most diverse geological landscapes in the world, where sections representing most of the Earth's history are accessible. Outcropping bedrock formations in Svalbard range from the Archaean to Quaternary in age and were uplifted during the Cenozoic era (Koevoets et al., 2019). Geologically, the peninsula is part of the contact zone of two large structures of the first order: the horst-anticlinorium of the western coast of Spitsbergen and the West Spitsbergen graben. Quaternary deposits (soft sediment) consist of isostatically raised marine sediments in the lowlands, glacial and glacio-fluvial deposits in the valleys, extensive and complex slope deposits, areas of aeolian sediment cover, and extensive in situ weathering of bedrock. The landscape is particularly diverse: from watershed peaks to the landscapes of U-shaped valleys, extensive mountain plateaus, small valley glaciers and moraines, and coastal plains. Much of the terrain hosts marked mountain surfaces, steep slopes, and moraines draped by primary and Arctic desert soils with thin herbaceous–moss–lichen groups. All sediments and bedrock are heavily influenced by the perennial frost in the ground (permafrost) (Demidov et al., 2021). Over time, especially the more fine-grained deposits have accumulated an excess of ground ice, especially the upper 1–5 m of the permanently frozen soil (Gilbert et al., 2018).

The Nordenskiöld Land area was specifically chosen for this study because it represents the largest and most compact ice-free peninsula of the Svalbard archipelago, located between Isfjorden, Van Mijenfjorden, and Bellsund (Fig. 1c). It also represents the area where most of the human settlements (Longyearbyen and recreational huts in the vicinity, Barentsburg, and Svea – a mining city whose activities may be decommissioned soon) and infrastructure are located. In addition, there is a lot of transport by snowmobile and dog sledding during the winter season and movement on foot in this area for recreational and practical purposes. This makes the present study highly relevant from a societal point of view, considering that this century the Arctic will undergo the most rapid projected climate change than any other region around the globe (Ford et al., 2021).

Hydro-morphological hazards at middle to low latitudes are regularly mapped, and their information is freely shared in local and global databases. This is the case for co-seismic (Schmitt et al., 2017; Tanyaş et al., 2017) and rainfall-induced (Kirschbaum et al., 2009; Emberson et al., 2022) landslides, and the same is also valid for floods (Adhikari et al., 2010). The part of the geoscientific community working on cryospheric hazards has not yet produced global products, but current trends have seen an increase in data sharing, with thaw slump inventories often becoming part of supplementary materials in recent publications (Ramage et al., 2017; Lewkowicz and Way, 2019; Swanson, 2021; Nitze et al., 2018). Our aim here is to align with this movement and share the latest version of our TS and TEG inventories mapped for the Nordenskiöld sector in Svalbard. In Sect. 3.1, we provide a detailed description of the two inventories.

Moreover, another aspect differentiates research carried out at middle to low latitudes with respect to the trends in the Arctic context. In fact, hazard inventories have been commonly used for susceptibility modelling since the early years of 1970 (Brabb et al., 1972), and their results are presented as having both explanatory (Lombardo and Mai, 2018) and predictive (Lima et al., 2021) purposes. The explanatory element of these models is usually meant to interpret why they occur where they occur based on statistical relations between the locations where these hazards take place and their landscape and environmental characteristics (Steger et al., 2021). As for the predictive aspect of these models, they are used to probabilistically define areas where these processes may currently be absent, but their characteristics imply that they could manifest in the future (Reichenbach et al., 2018). As a result, decision-makers can plan suitable remedial actions, if needed, or assign land use development constraints (Roccati et al., 2021). High-Arctic environments have not received the same modelling attention with few exceptions (e.g. Blais-Stevens et al., 2015; Luoto and Hjort, 2005) despite their inarguably unique and pristine vulnerable landscapes threatened by global warming. Therefore, our intent is to expand the available literature on data-driven models applied to cryospheric hazards and demonstrate their potential as tools to understand local dynamics, as well as predict locations that will undergo the same surface deformation process.

The resulting inventories encompass 562 TSs and 908 TEGs. Compared to the previous preliminary study (Nicu et al., 2021a), the RTS inventory has increased from 400 to 562 polygons. As for the TEGs, the updated version of our inventory included 908 polygons, 98 more than were mapped in a previous study (Nicu et al., 2022c). This final effort brought our inventories to their current and final form, in which the mapping procedure covered the whole study area shown in Fig. 1, and field surveys have validated some of their positions and extent.

The inventories are of high value in a climate change context, as they can be of use to a wide range of scientists, such as geomorphologists, climatologists, hydrologists, biologists, and archaeologists, as well as stakeholders and local authorities, in their effort to quantify the potential impacts of the two hazards on infrastructure (Hjort et al., 2018, 2022) and cultural heritage (Nicu et al., 2021a, 2022c). To explore their characteristics for any of the users and uses mentioned above, below we will summarise the frequency area distributions (FADs) of the two inventories we mapped, and in the subsequent sections, we will present the results of the susceptibility modelling we performed.

A systematic TS and TEG mapping protocol to share these cryospheric hazards among researchers has yet to root within the geoscientific community. This work aligns well with other attempts to make data on TSs and TEGs freely accessible because we believe that the surface deformation dynamics of delicate environments laying within Arctic and peri-Arctic regions can be studied only as a collective effort. For this reason, we share our inventories in the hope of triggering similar behaviours within our community and stimulating the implementation of advanced models, as per other mid-latitude hydro-morphological processes.

Notably, until the use of automated mapping tools will become viable for cryospheric hazards, any manual mapping procedure such as the one we undertook here may suffer from subjectivity. To minimise any individual expert-based opinion and therefore remove its bias, in this work we implemented a collective mapping protocol in which two Arctic geomorphologists independently created the inventories only to be merged at a later stage. We believe this to be another requirement to be added to the collective effort we mention and recommend above. In fact, other studies have shown that collective mapping contributes to reducing uncertainties, which would otherwise become part of the data and propagate in any model one may build with it (Ardizzone et al., 2002).

Aside from the importance of a standard data-sharing platform within the global system, even just within the Svalbard context, this is something of great relevance. In fact, the study site we chose had undergone significant changes in recent times. The work of Ziaja (2001) has shown the extent of these changes in the form of permafrost degradation, whose dynamics can be better understood if framed within the bigger picture of the Svalbard meteorological settings.

In fact, Nordenskiöld Land has always been covered with a lesser glacier extent compared to the rest of the archipelago. This is due to the direction the maritime air masses follow in the area. Specifically, the effect of the warm West Spitsbergen Sea Current creates a convergence of mild and humid air from the south and chilly air from the north. This convergence results in a local micro-climate warmer than the rest of Svalbard and in general than what is typical at these latitudes. In addition to an already delicate situation, Ziaja (2001) observed that the deglaciation in Nordenskiöld Land has evolved at double the rate compared to Sørkapp Land (south Svalbard), arguing this to be an indication of a greater sensitivity of our study site to global warming. Therefore, we consider it vital to document and share evidence of permafrost degradation (our TS and TEG inventories) to reconstruct a baseline to which future monitoring protocols should refer for further exploring the effects of climate change in the area. One of the possible tools to use to explore these effects falls in the category of data-driven models, to which susceptibility studies belong. However, hardly any susceptibility studies have been carried out so far to estimate locations prone to TSs and TEGs in peri-Arctic regions (Blais-Stevens et al., 2015; Rudy et al., 2016; Veh, 2015).

Along this line of research, we proposed a tool for interpretable and flexible predictive models, offering the chance to explore the results from multiple aspects, among which we include a multi-hazard susceptibility assessment. The performance produced falls within the excellent class proposed by Hosmer and Lemeshow (2000). Therefore, standard practices would consider that such a model results in a piece of reliable information for local administrators to base their decisions on and plan a suitable course of action to reduce the risk due to these cryospheric hazards. This is already an important achievement; however, below we would like to stress a few elements that we already envision requiring further considerations to develop our model into an operational tool. Both TS and TEG processes are shown to be highly dependent on soft sediment characteristics, data which are so far lacking on Svalbard. Adding map data with the type and potential thickness of surface sediments would further increase the accuracy and detail of predictions. The other prominent issue we faced had to do with the absent temporal information in our inventory. This is something that unfortunately affects virtually all the TS and TEG inventories mapped across the globe. For this reason, we are limited to statically investigating and understanding locations prone to these hazards. However, this also raises the question of whether such information can be really used outside the academic context. In fact, any model without a temporal connotation will inevitably learn to mimic the process that occurred at the time of the orthophoto or satellite image used for mapping. In other words, no temporal information on temperature, rainfall, or other dynamic characteristics can be included in the model. Therefore, in a rapidly changing environment such as the Svalbard landscape, the probabilities of occurrences we estimated may have already been affected by global warming and permafrost degradation processes (Ziaja, 2004). With this in mind, we consider our workflow just a proof-of-concept of what can be achieved in the hope that in the years to come a broader scientific effort can bring together a fully spatio-temporal description of these cryospheric hazards. If this wish would become a reality, then a whole spectrum of different models and research questions will open for the geoscientific community to address. For instance, future simulations of TS and TEG probabilities at varying climate scenarios could be achieved by introducing, for instance, the temperature as a covariate and then using a plug-in simulation (Do et al., 2005; Lombardo and Tanyas, 2020) tool to project the change in susceptibility as the future temperature pattern changes. Fortunately, the status of the scientific branch focused on developing automated mapping tools has reached such a level of maturity that it is close to becoming widely adopted even in peri-glacial environments (Meena et al., 2022; Nava et al., 2022). For instance, the first article has already been published on the use of deep learning architectures for automated TS mapping (Huang et al., 2020). This represents a promising venue for multi-temporal mapping because each artificially intelligent mapper tool is run over a specific remotely sensed scene, and the same operation can therefore be repeated for each satellite orbit. Still remaining is the lack of spatially detailed and accurate data from the Arctic, where the processes discussed here required a ca. 5 m resolution for accurate detection of features to form a training dataset.

Another element that can be improved with future efforts has to do with the actual target of the model. So far, our aim was to estimate locations prone to TS and TEG formation. However, these processes also have a spatial extent, and the threat they may pose to local activities is equally if not more important than the simple notion of where they may initiate. For this reason, we already envision future models that would take the measured extent of TSs and TEGs as the response variable, this time solving a regression task rather than a classification one as per the susceptibility requirement. Such a direction has recently been explored for landslides occurring at lower latitudes (Lombardo et al., 2021; Moreno et al., 2022). An even better extension has already been tested in which the expectation of locations prone to landslides are modelled, together with the expectation of the resulting landslide size (Aguilera et al., 2022; Bryce et al., 2022).

Notably, all these methodological considerations are valid extensions to be tested within the Svalbard landscape. However, they can also be valid outside it. If space–time models do become a viable approach because multi-temporal inventories also become available, then dynamic simulations could also be extended to the whole peri-Arctic sector. This would enable large-scale considerations on climate change and its cascading influence from temperature to TS and TEG spatio-temporal patterns.

At a global level, permafrost is undergoing considerable degradation following the increasing trend of global warming. Recent studies highlighted the fact that the Arctic has warmed 4 times faster than the globe since 1979 (Rantanen et al., 2022). This leads to TS and TEG occurrences, which can pose a threat to Arctic infrastructure (Hjort et al., 2022) and cultural heritage (Nicu et al., 2021a, 2022c), impact the fluvial sediment budget (Lamoureux and Lafrenière, 2018), and release significant amounts of greenhouse gases, such as carbon dioxide and methane, to the atmosphere (Oberle et al., 2019; Ran et al., 2022). Cryospheric hazards are likely to further increase in the future following climate change (Ding et al., 2021), and using the latest statistical advances to predict their likely occurrences is of paramount importance. This study showed the importance of the two inventories and what can be achieved when using them both separately and together in a multi-hazard approach. The method can be adapted and transferred to the entire ice-free area of the Svalbard Archipelago and other circumpolar areas. The final multi-hazard map represents a valuable tool that can be further processed and improved for local authorities and policy makers (Nicu and Fatorić, 2023) and can be transformed into plans at various scales of mitigation and adaptation measures (Nicu, 2022).

The NPI images are freely available at https://geodata.npolar.no/ (NPI, 2022a). The digital elevation model is freely available at 10.21334/npolar.2014.dce53a47 (Norwegian Polar Institute, 2014). The Geological Map of Svalbard (Geologi Svalbard), in raster format, scale 1:250 000, is freely available at https://geodata.npolar.no/arcgis/rest/services/Temadata/G_Geologi_Svalbard_Raster/MapServer (NPI, 2022b). The TS and TEG inventories are publicly available in shapefile format at 10.1594/PANGAEA.945348 (Nicu et al., 2022a) and 10.1594/PANGAEA.945395 (Nicu et al., 2022b), respectively.

At a global level, permafrost is undergoing considerable degradation following the increasing trend of global warming. Recent studies highlighted the fact that the Arctic has warmed 4 times faster than the globe since 1979. To better understand what the expectations of future permafrost degradation-related processes are, a systematic sharing practice of the mapping routines we perform as a community should become commonplace. In line with this objective, in this work, we share the TS and TEG inventories we mapped and validated through several field campaigns. Moreover, to better understand these processes and attempt to reliably predict them, the implementation of data-driven models holds promising potential. This is also the case for cryospheric hazards such as TSs and TEGs, whose occurrence probability we propose here to be modelled via a binomial GAM. We also take it a step further and produce a multi-hazard susceptibility map of our test site in Nordenskiöld Land. These types of models are also rare in peri-Arctic environments, and their spread may lay the foundations to build a global assessment of cryospheric hazards' development as a function of global warming. This is the direction we consider to be crucial for assessing the risk that Arctic communities may soon be exposed to. This is something of fundamental importance because the changes we have witnessed in the recent past and that we see today will be relatable to the changes we will see in other permafrost-rich areas such as the Alps or the Himalayan range. Their global warming has yet to reach the extent of the change we have observed so far near the pole and therefore in Svalbard.