Increased exposure of the shores of Hornsund (Svalbard) to wave action due to a rapid shift in sea ice conditions

Abstract

Negative trends in sea ice extent in polar regions lead to increasing exposure of the coasts to wind-generated waves and thus to wave-induced erosion. In the Northern Hemisphere, a region undergoing particularly rapid changes is the Barents Sea, contributing nearly one-fourth of the total sea ice loss in the Arctic. This work concentrates on the westernmost edge of that area: the Hornsund fjord, located in the southwestern part of Spitsbergen (Svalbard). Long-term (1979–2023) variability in sea ice and waves offshore and in the coastal zone was analyzed based on sea ice reanalysis data, wave observations at three coastal locations, and a spectral wave model. We found that sea ice concentration at the entrance to Hornsund underwent a “regime shift” in 2005, from winters with frequent compact-ice occurrence in the period 1979–2005 to almost ice-free winters in the period 2006–2023. Results of simulations with a spectral wave model calibrated to observations in ice-free periods show large biases during compact-ice events (strongly overestimated wave height and energy flux, slightly underestimated peak and energy period), suggesting significant influence of ice-related attenuation on wave conditions nearshore. These biases, combined with the sea ice and wave data, were then used to estimate the mean seasonal cycles of nearshore wave conditions in the two periods 1979–2005 and 2006–2023. The results show that the lack of sea ice in the recent two decades has led to a substantial increase in wave energy reaching the coastal zone (up to 100% between February and April), and to a shift of the seasonal maximum of that energy from late autumn (November–December) to winter (December–March). Overall, these changes indicate an increased exposure of the coasts to wave-induced erosion and sediment transport.

1. Introduction

One of the important consequences of the recent climate-change-related sea ice decline in the Arctic, and of the associated expansion of open-water areas (Barnhart et al., 2016), is increasing wind wave action (e.g., Stopa et al., 2016; Casas-Prat and Wang, 2020). Because of longer fetch, in some regions combined with more intense and/or more frequent storms, wind-generated waves tend to have larger amplitudes (and thus energy) and periods (and thus lengths and propagation speeds). In semi-enclosed shelf seas of the Arctic, as, for example, in the Beaufort, East Siberian, or Kara seas, most of this excess wave energy is dissipated at the boundaries of those regions, that is, either within the surrounding sea ice pack or at the coasts. As a result, Arctic coasts are becoming more and more vulnerable to wave-induced erosion, inundation, and redeposition of sediments (e.g., Barnhart et al., 2014; Irrgang et al., 2022; Nielsen et al., 2022).

Among the Arctic regions most affected by climate change is the Barents Sea (Gerland et al., 2023). In spite of its small area, it contributes approximately 24% to the total observed sea ice loss in the Northern Hemisphere (Onarheim and Årthun, 2017). Negative trends in Barents Sea ice extent, concentration, and thickness are correlated with, among other things, changes in ocean stratification and positive temperature trends of both the ocean and the atmosphere—a set of processes and feedbacks that are often collectively referred to as “Atlantification” (Polyakov et al., 2017). These Barents Sea trends are a result of combined external influences (e.g., sea ice advection from the north and east, and advection of warm Atlantic waters from the southwest) and internal variability of the local ocean–sea ice–atmosphere system (Siew et al., 2024). Crucially for further discussion in this article, a net effect of all those factors was a rapid change of conditions around the year 2005. At the scale of the whole Arctic, 2005 marks the change of sign of the internal Arctic mode (AM) index (Zhou et al., 2024). The AM, defined as the dominating mode of the surface temperature variability north of 40°N, has maximum amplitudes over the eastern and central Arctic and correlates negatively with sea ice concentration there (see figure 4 in Zhou et al., 2024). The AM values were negative from the late 1970s to 2005 and remained positive after the change of sign in 2005. As the simulations by Zhou et al. (2024) show, this switch in the internal variability of the Arctic system explains the observed rapid acceleration of the Arctic climate change in the last two decades. Not surprisingly, a signature of the AM change around 2005 can be found in diverse Arctic-wide and regional observational datasets, including Barents Sea ice extent and sea surface temperature (Barton et al., 2018), volume of sea ice import to the Barents Sea (Lind et al., 2018), relationships between wintertime Barents Sea ice coverage and summertime Atlantic water temperature (Schlichtholz, 2021), Barents Sea ice thickness (Onarheim et al., 2024), fast-ice coverage in Svalbard fjords (Muckenhuber et al., 2016), and a number of freezing degree days in Svalbard (Urbański and Litwicka, 2022).

The processes and trends described above have a direct influence on the sea ice variability west of Spitsbergen, in the main area of interest in this study. Sea ice pack originating in the northern Barents Sea, to the east and southeast of Svalbard, is the dominating ice type occurring along the western coasts of Spitsbergen and within the open, central parts of Hornsund, Bellsund, and the fjords further north. This sea ice drifts with the Sørkapp Current around the southern tip of Spitsbergen and forms a narrow strip bounded by the coast on the eastern side and by the warmer Atlantic waters carried by the West Spitsbergen Current on the western side. Although the width of this sea ice zone rarely exceeds 20–30 km, it is known to play an important role in protecting the coasts from intense autumn and winter Atlantic storms (Zagórski et al., 2015).

In this study, we use sea ice reanalysis data to demonstrate that the long-term (1979–2023) variability of sea ice conditions along the west coast of Spitsbergen largely corresponds to the trends observed in the Barents Sea described above. We concentrate on a region at the entrance to Hornsund, that is, an area relevant for wave energy entering the fjord, and show that the changes of sea ice concentration observed there can be characterized as a rapid shift between two markedly differing periods—before and after 2005—rather than a gradual change. In other words, the analyzed region rapidly switched from ice-covered to almost entirely ice-free winters. The main goal of this study was to estimate the consequences of that change for wave energy reaching the coasts of Hornsund. This issue is critical for assessing the vulnerability of the fjord to wave-induced erosion in the new, ice-free regime, especially considering that most storms in the analyzed region occur in the cold season, between November and April (Wojtysiak et al., 2018).

Our study is based on an analysis of wave measurements from three coastal locations within Hornsund, combined with spectral wave modeling. We show that the model run without any sea ice input reliably reproduces the observed wave characteristics in ice-free periods, and that the modeling results are significantly biased when high-concentration ice is present, indicating attenuation of wave energy and the corresponding decrease of wave heights and increase of mean wave periods. We use the differences between the model and observations from the periods with ice, together with a seasonal cycle of waves and long-term statistics of sea ice before and after 2005, to estimate differences between those two time periods in terms of the seasonal cycle of wave energy flux reaching the shores. Finally, we discuss the likely consequences of those differences for coastal erosion and other dynamic processes nearshore.

2. Area of study

Hornsund is the southernmost, relatively small (length approximately 30 km) fjord of west Spitsbergen, Svalbard Archipelago, with several side fjords and bays, and a complex bottom topography (Figure 1). For wind wave propagation and evolution, important features are large water depth gradients and, in many areas, presence of numerous shallows and skerries. The overall circulation is cyclonic (Jakacki et al., 2017), with strong influence of tides (Kowalik et al., 2015). In nearshore locations, tidal currents may reach 2 m s⁻¹, and tidally induced water level changes modulate wave dissipation and propagation speed and thus wave properties (Herman et al., 2019). Due to the fjord’s limited size and complex coastline, locally generated waves associated with prevailing easterly winds are fetch-limited and thus small, although they might reach substantial steepness. Due to Hornsund’s wide and deep connection to the ocean (about 12 km and over 100 m, respectively), its wave conditions are dominated by waves entering from the open ocean. The wave climate is characterized by a pronounced seasonal cycle: storm waves tend to occur between late autumn and spring, and summer months are swell-dominated (Bertin et al., 2013; Semedo et al., 2015; Wojtysiak et al., 2018). The dominant wave directions are from the southwest; that is, during a typical storm, the northern coasts of Hornsund receive more wave energy than the southern ones (Herman et al., 2019). In particular, the area of Isbjørnhamna and Hansbukta, where the Polish Polar Station is located (Figure 1), belongs to the most exposed stretches of the coast.

Figure 1.

Area of study.

(A) Svalbard Archipelago with the M1 model boundary and location of the six ERA5 sea ice concentration data points at the entrance to Hornsund fjord. (B) Hornsund fjord with the M2 model boundary and the three wave data stations. Background maps: IBCAO V5.0 Grid at 100 m and Norwegian Hydrographic Service at 5 m for bathymetry, Norwegian Polar Institute for land and glacier extent.

As in other Svalbard fjords, various types of ice can be found in Hornsund, depending on the season as well as local and regional weather and oceanic conditions. In periods of intense calving of marine-terminating glaciers, substantial amounts of glacier ice can be adrift in the fjord and accumulate at the coasts, especially in relatively shallow and sheltered bays. In the cold season, typically between January and June, fast ice and drifting forms of locally generated sea ice are present, mostly in the inner bays of east Hornsund (Swirad et al., 2024; Text S1). As mentioned in the introduction, an allochthonous sea ice pack carried with ocean currents from the Barents Sea is the most relevant of the ice types for wave conditions in Hornsund. Its presence in the central parts of the fjord is characterized by strong temporal variability at interannual, seasonal, and daily scales (Swirad et al., 2024). Finally, the ice foot is occasionally present at various parts of the coast—an ice form that has no influence on waves, but plays a very important role in protecting the shores from wave-induced erosion (Rodzik and Zagórski, 2009).

3. Data and methods

3.1. Sea ice data

The main source of sea ice concentration data used in this work is the ERA5 reanalysis (Hersbach et al., 2023). The ERA5 data are available hourly since 1948 on a 0.25-degree spherical grid. Here, we have used sea ice concentration from the “satellite era,” that is, 1979–2023, from six grid meshes at the entrance to Hornsund (Figure 1). The average sea ice concentration from those locations, denoted with C, was used as a bulk measure of ice conditions in the area.

The choice of ERA5 as a sea ice data source is motivated by its continuous availability over a sufficiently long time period. The drawback, however, is the low spatial resolution, which might be problematic considering that sea ice in the region of interest (and along the west Spitsbergen in general) occurs only within a narrow strip along the shore. In order to test the reliability of ERA5 sea ice data for our purposes, we performed validation for the period 2018–2023 against high-resolution (1 km) data from sea ice charts of the Norwegian Meteorological Institute (MetNo, 2023). The charts, based on manual interpretation of satellite data from various sources (radar, optical, and infrared images), are available on weekdays and show sea ice concentration classes defined by the World Meteorological Organization (WMO).

The ERA5–MetNo intercomparison was performed for an area covering the six ERA5 grid cells used in the rest of the analysis. The results are shown in Figure 2. Although many situations with low-concentration sea ice are not captured by the ERA5 dataset, leading to the overall correlation coefficient of only 0.72, the great majority of situations with compact ice pack, that is, those which are relevant for wave propagation, are present in both datasets. (Notably, when only nonzero ERA5 values are taken into account, the correlation coefficient increases to 0.84.) Thus, the ERA5 data are suitable for the purpose of this study. On average, ERA5 values are underestimated relative to those from MetNo by approximately 16%. We divided the average ERA5 sea ice concentration into “loose” for C < 0.5 and “compact” for C > 0.5 (see Figure 2 and Section 4.2 for details on how this value was determined) which is roughly consistent with the boundary between open and close drift ice in the WMO scheme set at ice concentration of 0.7.

Figure 2.

Intercomparison between the sea ice concentration C from the ERA5 and MetNo datasets.

(A) Time series in the period February 2015 to July 2023 (note that data from sea ice charts of the Norwegian Meteorological Institute, MetNo, are available from January 2018), and (B) a corresponding scatterplot. In (A), horizontal dashed lines mark the boundaries between the “loose” and “compact” ice in the two datasets (see text for details), and black lines show the time range of measurements at the three stations GAS, HBK, and VES. In (B), n denotes the number of data points in each quadrant.

3.2. Wave observations

Measured wave energy spectra from three stations within Hornsund (Figure 1) are used in this study: one located in the southern part of the fjord, west of Gåshamna (GAS; 76.9506°N, 15.7710°E, 22 m depth), and two at the opposite side, in Veslebogen (VES; 76.9951°N 15.4881°E, 16 m depth) and in Hansbukta (HBK; 77.0031°N, 15.6298°E, 22 m depth). A summary of measurements is provided in Table 1; a detailed description of the data processing and instruments used can be found in Swirad et al. (2023) and in Text S2.

Table 1.

Summary of observational data used in the study

Station Name	Longitude (°E)	Latitude (°N)	Mean Water Depth (m)	Time Period	No. of Data Points	Station IDs in SMH23a
GAS	15.7710	76.9506	22.5	Jun 5, 2018–Jan 14, 2021	22,560	GAS4, GAS5
HBK	15.6298	77.0031	22.0	Jun 10, 2015–Jan 15, 2019	30,208	HBK6–HBK10
VES	15.4881	76.9951	16.0	Jun 5, 2018–Feb 12, 2021	23,256	VES2, VES3

^aCorresponding station IDs used in the paper by Swirad et al. (2023).

3.3. Spectral wave modeling

As in Herman et al. (2019), wave modeling in this study is based on the spectral wave model called SWAN for Simulating WAves Nearshore (SWAN Team, 2024). Version 41.45A of the model was used on nested grids denoted with M1 and M2 (Figure 1). The domain of model M1 covers a wide region west and southwest of Spitsbergen and provides boundary conditions for the local model of Hornsund (M2). Both models are forced with 6-hourly 10-m wind speeds from the NCEP Global Forecast System (GFS; National Centers for Environmental Prediction, 2015). Wave energy spectra at the boundary of model M1 come from the Arctic Ocean Wave Hindcast (2024). Their spatial and temporal resolutions equal 3 km and 1 hour, respectively. In model M2, spatially uniform but temporarily variable water levels are assumed. Hourly time series of water levels are obtained from the Arctic Ocean Tidal Forward Model (AODTM-5; Padman and Erofeeva, 2004). In M1, no water level variations are taken into account.

All model settings related to parameterizations of physical processes and to numerical integration of the governing equations are identical to those used in Herman et al. (2019). They are not described here, but a summary of model settings can be found in Table S1. Crucially, no sea ice information is taken into account as input to the wave models. The underlying idea is, first, to use the modeling results from ice-free periods in order to show that the model reliably reproduces the observed wave characteristics at the three stations mentioned in the previous section, and second, to use the differences between the observed and simulated wave properties in periods with ice in order to quantify, in a statistical sense, the influence of the ice pack on waves. Obviously, this part of the analysis was done for the time period in which observations are available, that is, between June 2018 and January 2021 for station GAS, between June 2018 and February 2021 for station VES, and between June 2015 and January 2019 for station HBK (see Table 1). Additionally, in order to obtain robust statistics of the seasonal cycle of wave characteristics in the area of study (Section 4.1), the simulations were performed over an 8-year-long period from July 2015 to June 2023.

3.4. Analyzed wave characteristics

In the remaining parts of the article, we concentrate on four bulk wave characteristics that are particularly relevant from the point of view of wave-induced coastal processes, including wave setup, swash and runup, nearshore sediment transport, and so on. These are: the significant wave height H_s, the peak period T_p, the energy period T_e, and the wave energy flux P_w (e.g., Holthuijsen, 2007). H_s and T_p are the two wave properties most often used in (semi)empirical formulae for estimating wave runup and setup (see Gomes da Silva et al., 2020). T_e, derived from the zeroth and first negative moments of the wave energy spectrum, is the period corresponding to the weighted average of wave energy. Together with H_s, it is used, among other things, in an approximate formula for the (deep water) wave energy flux, in which P_w ∼ H_s²T_e. Here, we computed P_w in an exact way, that is, by integrating the product of wave energy and group velocity over the whole range of wave frequencies and directions (e.g., see Jiang et al., 2022). As a measure of the rate of transfer of wave energy per unit length of the wave front, P_w is a key measure of the wave energy reaching the coastal zone—and thus being dissipated nearshore through bottom friction, wave breaking, runup, sediment transport, and so on (e.g., Harley et al., 2017; Mentaschi et al., 2017).

4. Results

4.1. Variability of sea ice and wave conditions in the area of study

Not surprisingly, the timing of the rapid qualitative change in sea ice conditions in the area of study coincides with regional and larger-scale ocean–sea ice–atmosphere changes described in the introduction, including Barents Sea temperature and sea ice trends (Figure 3A). Figure 3B shows the daily ERA5 sea ice concentration C at the entrance to Hornsund in the years 1979–2023. In spite of a strong short-term and year-to-year variability, differences between the earlier and later part of that period are clearly visible. Before 2005, sea ice typically appeared in November and did not disappear before June. After 2005, several winters were completely ice-free, and winters 2010/2011 and 2019/2020 were the only ones with notable amounts of high-concentration ice. A negative trend in the yearly number of days with ice is present throughout the entire analyzed period. In 1979–2005, it equals −2.2, −2.6, and −0.8 days per year for ice concentration C exceeding 0.3, 0.5, and 0.7, respectively (dashed lines in Figure 3C). Remarkably, however, this trend does not continue with a similar amplitude after 2005. Instead, a discontinuity is observed that manifests itself both in the length of the ice season, which after 2005 rarely begins before January and often ends already in April, and in the occurrence of compact ice (C > 0.5; Figure 3D). While in 1979–2005 high-concentration ice was present on more than 50% of days between January and April, its occurrence frequency in the same months dropped to below 10% in 2006–2023.

Figure 3.

Air temperature and sea ice conditions in the area of study.

(A) Mean winter 2 m air temperature T_a and sea ice concentration C in the northern Barents Sea east of Svalbard (data from Gerland et al., 2023), and (B–D) sea ice concentration at the entrance to Hornsund in the period 1979–2023: (B) daily ice concentration C in the period 1979–2023; (C) the total number of days with ice in individual years; and (D) the average fraction of days per month with compact ice (C > 0.5) in the two sub-periods 1979–2005 and 2006–2023. In (A), dashed lines show the linear trend in the periods 1979–2005 and 2006–2020. In (B), for better legibility days with C = 0 are shown in white. In (C), the three colors of continuous lines correspond to ice concentration exceeding the value of 0.3 (yellow), 0.5 (blue), and 0.7 (red); the dashed lines show the linear trend in the period 1979–2005. In (D), continuous lines with circles show the mean over individual years, and the thin dashed lines show the mean ± one standard deviation.

Crucially for the coastal zone within Hornsund, the sea ice and the storm seasons in the area around Svalbard coincide: the highest and longest waves (Figure 4) are observed between November and April, that is, in the period when the probability of sea ice occurrence is the highest. In the summer, wave heights at the three analyzed stations never exceed 3 m and are lower than 1 m for more than 95% of the time. This “stormy winter and spring, quiet summer” pattern is typical for the Norwegian and Barents Sea waves (e.g., Atkinson, 2005). Importantly, the seasonal cycle of wave activity is most pronounced in the case of the wave energy flux P_w (Figure 4C). As P_w is approximately proportional to H_s² and T_e (see Section 3.4), and both H_s and T_e vary seasonally, the mean and extreme values of P_w in winter are several times (up to an order of magnitude) higher than in the summer. Thus, in an ice-free regime for which these statistics were computed, the coast of Hornsund is exposed to substantial energy fluxes associated with high waves from the open ocean—and vice versa, when present, the ice has the potential to markedly reduce those fluxes by attenuating part of the incoming wave energy.

Figure 4.

Seasonality of wave conditions at the three analyzed stations.

(A) Significant wave height H_s, (B) energy period T_e, (C) wave energy flux P_w, and (D) peak period T_p at stations GAS (blue), HBK (red), and VES (yellow). The symbols correspond to the mean, the 95th percentile p₉₅, and the maximum value for a given month (see legend in panel A) based on data from the 8-year period from July 2015 to June 2023. Note that the y axis in (C) is logarithmic. The statistics for all months are computed from modeling results, that is, they represent an ice-free regime.

For the quantitative estimation of the role of sea ice (see further Section 4.3), it is important that, although high waves and sea ice occurrence are correlated at the seasonal scale, individual storm events and compact ice presence within cold seasons can be treated as independent, that is, the chance of storm waves and compact ice occurring at the same time can be estimated from the probabilities of those two types of events alone. We confirm this independence between waves and ice by analyzing time series of C and offshore H_s from the ERA5 data (at a point located at 12°E, 76.52°N, at all times outside of the sea ice zone): the probability distributions of H_s values from the November–June seasons corresponding to time instances without and with ice can be regarded as the same (a Kolmogorov–Smirnov test fails to reject this hypothesis at the significance level of 5%). This result might seem surprising: ocean waves entering sea ice modify it in a number of ways, including radiation stress, drift, breaking, rafting and piling up of ice floes, intensified melting due to enhanced oceanic mixing, and so on (e.g., Dumont, 2022; Thomson, 2022). As the intensity of all those processes increases with increasing wave action, one might expect that their net effect would manifest itself in a statistically significant correlation between H_s and C. Apparently, different combinations of all relevant factors—ice properties, incoming waves characteristics, as well as local wind speed and direction, currents, temperature, and so on—modify ice concentration in different ways, leading to the observed lack of a H_s–C relationship.

4.2. Influence of sea ice on the observed wave characteristics

As described in Section 3.2, all available wave observations from Hornsund come from the recent time period, that is, they represent ice-free conditions over most of the time, even in winter. Still, the data from stations GAS and VES capture the most “icy” winter of the period 2006–2023, that of 2019/2020, while a few short sea ice episodes in early 2017 and early 2018 are captured in the data from HBK (Figure 2A). Considering the limited number of situations with ice, we did not attempt to formulate any quantitative relationships between ice concentration and wave attenuation. Instead, as already mentioned in Section 3.1, we divided situations with ice into two groups, henceforth referred to as “loose ice” and “compact ice.” The underlying assumption, based on existing observations of wave–sea ice interactions, is that the influence of ice on waves is insignificant at low C, and increases rapidly when a certain critical value of C, here denoted with C_cr, is exceeded. At C below C_cr, ice floes hardly interact with each other, so that individual floes may follow the wave motion, resulting in very low within-ice and ice–water stresses, and thus very weak wave energy attenuation. To the contrary, at C above C_cr, floes are densely packed and several wave energy dissipation mechanisms, both within the ice and in the under-ice boundary layer, lead to significant net wave attenuation.

According to the above assumptions, the value of C_cr is established such that, first, all situations with loose ice result in model–observations bias as close as possible to that with C = 0, and second, the difference between the model–observations bias for loose and compact ice is as high as possible. In our case, we find C_cr to lie between 0.5 and 0.6—values from this range produce very similar results. As the number of situations with C > C_cr is very small and, obviously, decreases with increasing C_cr, we set C_cr = 0.5 in the further analysis. This choice does not in any way influence the conclusions from this study.

The statistics of the model performance for the three classes of “no ice” (C = 0), “loose ice” (0 < C < 0.5), and “compact ice” (C > 0.5) are shown in Table 2 and, in the form of scatterplots, in Figure 5. When no ice is present, the results are best for station HBK. This fact can be attributed to the shallow and highly variable bathymetry in the areas surrounding the remaining two stations: details of that bathymetry have noticeable influence on wave propagation and dissipation, but cannot be resolved on the model grid used. Generally, however, the model satisfactorily captures the variability of wave conditions at all three locations. As already discussed in Herman et al. (2019), SWAN accurately predicts the total wave energy (and thus H_s) and the peak period (with a slight tendency to overestimation in the range of high T_p values), but tends to underestimate the energy period, which is extremely sensitive to the distribution of energy within the spectrum: even slight changes of the spectral shape lead to large changes of T_e. Crucially, the wave energy flux is reliably reproduced, especially in the range of high values, relevant for coastal erosion and other processes. These observations largely remain valid for situations with loose ice.

Figure 5.

Scatterplots of the observed and simulated wave characteristics for the three analyzed stations.

Significant wave height H_s (panels A, E, and I), energy period T_e (panels B, F, and J), peak period T_p (panels C, G, and K), and wave energy flux P_w (panels D, H, and L) at stations GAS (panels A–D), HBK (panels E–H), and VES (panels I–L). Colors (legend in panel A) show situations without ice (blue), with loose ice (yellow), and with compact ice (black). Note that the axes in panels D, H, and L, unlike in the remaining plots, are logarithmic.

Table 2.

Statistics of the SWAN model performance at stations GAS, HBK, and VES for the three sea ice classes “no ice,” “loose ice,” and “compact ice”

Statistics	No Ice				Loose Ice				Compact Ice
	Hs (m)	Te (s)	Tp (s)	Pw (kW m–1)	Hs (m)	Te (s)	Tp (s)	Pw (kW m−1)	Hs (m)	Te (s)	Tp (s)	Pw (kW m−1)
GAS
No. of points	19,641				2,689				230
Corr. coef.	0.81	0.63	0.78	0.83	0.56	0.40	0.67	0.52		0.52	0.52	0.33
Mean err.	0.003	−1.56	−0.45	0.006	0.040	−3.09	−1.03	−0.053	0.137	−5.00	−1.95	0.13
Mean rel. err.	0.30	−0.13	−0.03	6.2	1.08	−0.22	−0.07	8.00	2.68	−0.33	−0.12	11.86
Median rel. err.	−0.09	−0.12	−0.02	−0.30	0.16	−0.21	−0.03	0.02	2.23	−0.34	−0.08	5.33
HBK
No. of points	26,502				3,556				150
Corr. coef.	0.92	0.73	0.84	0.86	0.94	0.71	0.81	0.95	0.65	0.15	0.65	0.69
Mean err.	0.001	−1.41	−0.26	−0.13	0.02	−1.83	−0.48	−0.04	0.13	−4.30	−1.23	0.13
Mean rel. err.	0.05	−0.12	−0.02	0.13	0.20	−0.16	−0.03	0.92	4.52	−0.32	−0.10	37.9
Median rel. err.	−0.01	−0.13	−0.02	−0.15	0.04	−0.15	−0.03	−0.10	1.93	−0.33	−0.09	5.08
VES
No. of points	20,337				2,689				230
Corr. coef.	0.92	0.69	0.82	0.89	0.82	0.45	0.66	0.90	0.75	0.58	0.69	0.74
Mean err.	−0.04	−1.13	−0.18	−0.3	0.05	−2.67	−0.78	−0.03	0.16	−4.02	−1.76	0.20
Mean rel. err.	0.01	−0.10	−0.01	0.98	1.43	−0.19	−0.06	20.6	2.83	−0.26	−0.12	14.2
Median rel. err.	−0.13	−0.10	−0.01	−0.31	0.15	−0.17	−0.03	0.16	1.84	−0.24	−0.07	5.57

When compact ice is present, the situation is markedly different. The correlation coefficients between the modeled and observed values decrease, and the model bias increases: toward positive values in the case of H_s and P_w, and, to a much lesser extent, toward negative values in the case of T_p and T_e (Table 2). Qualitatively, these effects are expected and can be attributed to the frequency-dependent attenuation of wave energy in sea ice. In order to quantify their statistical significance, we perform a bootstrapping procedure described below for each analyzed variable X (where X stands for H_s, T_e, T_p, or P_w) and for each station S (where S stands for station HBK, VES, or GAS). We concentrate on the relative bias b_r, defined as b_r = (X_mod − X_obs)/X_obs, the statistic that, based on the underlying physics, can be expected to act as a measure of the effective strength of wave attenuation in ice, and that is most relevant for the analysis in Section 4.3. The goal is to ensure that the disproportion between the situations with no ice and with compact ice can be ruled out as a cause of the observed differences in model performance statistics. This disproportion is related to the small number of cases with compact ice versus those without ice, but also to the range of values of X captured by them (compare the blue and black dots in the scatterplots in Figure 5).

Let us denote with X_S,ni and X_S,ci the datasets of b_r of variable X at station S corresponding to situations with no ice and with compact ice, respectively. Let us also denote with n_S,ci the number of data points in X_S,ci. In the bootstrap procedure, the following steps are repeated N_b = 1000 times for each X and each S: (i) we sample at random n_S,ci values from the set X_S,ni and denote this set with X_S,ni,b; (ii) we perform a two-sample Kolmogorov–Smirnov test, at the significance level α = 0.01, comparing X_S,ni,b with X_S,ci; and (iii) we perform a Wilcoxon rank sum test, at the significance level α = 0.01, comparing the medians of X_S,ni,b with X_S,ci. Then the whole procedure is repeated with the difference that only values from X_S,ni that fall in the range of values in X_S,ci are taken into account. The results of all tests are unequivocal. For all X and all S, the hypotheses that the analyzed probability distributions (pdfs) are the same and that they have equal medians can be rejected at the significance level mentioned above: in all 1000 cases in the case of H_s, T_e, and P_w, and in more than 982 out of 1000 cases in the case of T_p (values vary slightly between stations and tests). Thus, the model biases in compact-ice situations can be treated as robust and used in the analysis of ice influence on wave parameters.

4.3. Estimation of differences between the past and present wave climate in Hornsund

Based on the model–observations biases in situations with compact ice, estimating differences in the seasonal cycles of the analyzed wave characteristics in Hornsund before and after the “regime shift” in 2005 is possible. To this end, two assumptions were made: first, that the influence of sea ice with a given concentration C on waves in the past was, statistically, the same as in the observation period; and second, that the wave variability and compact sea ice presence at the entrance of Hornsund are uncorrelated and were uncorrelated in the past. The first assumption amounts to assuming that the properties of “compact ice” in terms of its ability to attenuate wave energy were the same in both periods—we discuss this issue and its possible impact on the results in the discussion section. The second assumption has already been discussed in Section 4.1.

The main statistic of interest in this part of the analysis is the relative bias b_r in situations with C > 0.5. Figure 6 shows histograms of b_r for all analyzed variables from HBK, GAS, and VES. They are very similar at all three stations and therefore, for the sake of simplicity, we approximate them, for each variable, with the same pdf, fitted to the combined data from all stations (red histograms and black curves in Figure 6). In the case of T_e and T_p, Gaussian pdfs provide a good fit. In the case of H_s and P_w, the pdfs are strongly skewed and can be well fitted with generalized extreme value distributions. Notably, the strong skewness of these pdfs explains the large differences between the mean relative bias of H_s and P_w at the three stations, seen in Table 2: the mean values in this case are extremely sensitive to very large values in the tails of the pdfs, although the pdfs for individual stations have very similar medians and widths. The pdfs in Figure 6 also show that, as might be expected, the relative bias of the wave energy flux can be attributed almost entirely to the biases of wave energy. For instance, the mode of the pdf for H_s is located at b_r ≃ 1.5, and that for P_w at b_r ≃ 2.2 ≃ 1.5², as expected from the approximate relationship between H_s and P_w.

Figure 6.

Histograms of the relative bias b_r between the observed and simulated wave characteristics.

(A) Significant wave height H_s, (B) energy period T_e, (C) wave energy flux P_w, and (D) peak period T_p in situations with compact ice (C > 0.5) for stations GAS (green), HBK (yellow), and VES (blue). The probability distributions (black) are fitted to the combined datasets, shown in red: the generalized extreme value (GEV) distributions in the case of H_s and P_w (panels A and C), and Gaussian distributions in the case of T_e and T_p (panels B and D).

In the following, we use the simulated H_s and P_w data from the station HBK (as the seasonal cycles of waves at the three stations are very similar, the conclusions are valid for the remaining two stations as well and, more generally, for other nearshore locations of the central Hornsund). Combined with the seasonal cycles of the occurrence probability of compact ice before and after 2005 (Figure 3D), and with the pdfs of relative model biases obtained in the previous step, the data can be used to estimate the seasonal cycles of wave characteristics in (i) a completely ice-free regime; (ii) an ice regime of 1979–2005, and (iii) an ice regime of 2006–2023. The algorithm is as follows: (1) from the simulated values of variable X (H_s or P_w) at station HBK we select those that correspond to a given month m (m = 1, …, 12); the pdf of those data characterizes the ice-free regime (red lines in Figure 4A and C); (2) making use of the independence between sea ice and waves discussed above, we sample uniformly at random a subset of the data from step 1 corresponding to the mean fraction of days with compact ice in month m in the years 1979–2005 (blue line in Figure 3D); (3) using the definition of b_r, we estimate the “observed” values X_o for that subset as X_o = X_m/(1 + b_r), where b_r values are drawn from the relevant pdf (black lines in Figure 6A and C); this results in the pdf of X in month m in the period 1979–2005; (4) we repeat steps 2 and 3 for the years 2006–2023, using the fraction of days with compact ice representing that period (red line in Figure 3D). The resulting wave statistics for the three ice regimes are shown in Figure 7.

Figure 7.

Comparison between the three ice regimes considered, at station HBK.

Estimated statistics of (A and C) significant wave height H_s and (B and D) wave energy flux P_w under the “no ice,” “ice 1979–2005,” and “ice 2006–2023” conditions. Panels A and B show the seasonal cycles of the mean (dashed lines) and 95th percentiles (continuous lines). Panels C and D show the cumulative probability distributions for two selected months, February (continuous lines) and April (dashed lines).

Based on these estimates, the wave seasonal cycle in the last two decades, although affected by ice to some extent, has been very close to that typical for completely ice-free conditions. In winter months, these conditions are substantially different from those in the period 1979–2005. Especially between February and April, both the mean and the extreme values of H_s and P_w before 2005 were at the level of about 50% of those without ice. Importantly, the time of maximum wave activity has shifted from November–December in the period 1979–2005 to December–March in 2006–2023, that is, from late autumn to (largely ice-free) winter. Overall, the seasonal variations of wave conditions are strongly enhanced when sea ice is absent.

5. Discussion and conclusions

This work has shown that, in terms of sea ice presence, the coastal regions of the southwest Spitsbergen underwent a rapid change in recent years toward essentially ice-free conditions, with considerable consequences for the nearshore wave climate. The magnitude and rapidity of those changes most likely result from a combination of several groups of factors: one being negative ice concentration, thickness, and (presumably) floe-size trends in the source region of the ice pack drifting into the area of study (Barton et al., 2018); another, increased melting associated with advection of relatively warm Atlantic water masses (e.g., Arntsen et al., 2019) and yet another, atmospheric warming (Osuch and Wawrzyniak, 2016). Mutual strengthening of these factors—for example, faster melting and wave-induced “erosion” of smaller and thinner ice floes—likely produced the critical-threshold effect observed in 2005.

When assessing the differences between the past and present wave climate in Hornsund obtained in this study, it is important to remember that they are likely underestimated rather than overestimated. Several factors that might further enhance these differences were not taken into account in our analysis. First, we assumed that the offshore wave climate remained constant throughout the analysis period, whereas reanalysis data show small, but statistically significant positive trends in the strength and frequency of storms in the regions west of Svalbard (Wojtysiak et al., 2018). Second, one can reasonably assume that not only sea ice concentration, analyzed here, but also ice thickness before 2005 was greater than in recent years and, consequently, that the ability of sea ice with a given concentration C to attenuate wave energy was higher in the past than it is today (Sumata et al., 2023). Third, our observational data do not include situations with simultaneous occurrence of very large waves and compact sea ice. Therefore, our estimation of the relative model biases during storm events is an extrapolation from milder conditions—it amounts to an assumption that the processes involved are linear. In reality, due to the nonlinear character of wave–ice interactions, wave energy attenuation tends to be stronger when the waves are higher (all other factors being equal; for example, see Squire, 2018). In short, the final results in Figure 7 should be treated as conservative estimates—which makes them even more disconcerting.

When considering our results, one should remember that they are relevant for the central parts of Hornsund (roughly in the areas where the measurement stations are located) and that they describe wave conditions at the seaward boundary of the coastal zone, in 15–20 m water depth. The potential of the incoming wave energy to induce wave setup, sediment transport, erosion, and so on within that zone depends on many factors, including local bathymetry/lower beach morphology, characteristics of the beach material (grain size, etc.), as well as presence of other ice types not considered in this study.

Here, we have focused on pack sea ice at the entrance to the fjord which predominantly attenuates swell from the open ocean. However, different types of fjord ice (in situ, glacier, ice foot) play a role in wave energy delivery to the shores of Hornsund, notably by attenuating locally generated short wind waves from the inner fjord (easterly winds dominate in Hornsund) and by disabling waves access the beach itself (Rodzik and Zagórski, 2009). We found no significant correlation between this study’s C and ice coverage within Hornsund based on the binary ice/open water classification by Swirad et al. (2024), which means that ice conditions at the entrance and inside of the fjord are shaped by different factors and are largely independent of each other. While our method is suitable for reliably predicting wave properties at the three stations, the local (in-fjord) ice conditions should be considered when studying the more eastern and more coastal (depth < 15 m) areas. For instance, the fast ice in the inner bays of Hornsund (Burgerbukta, Brepollen, and Samarinvågen; see Figure 1) covered over 70% of the bay surface in March–May every year in 2015–2023 (Swirad et al., 2024) despite fast ice being affected by the “regime change” in 2005 (Muckenhuber et al., 2016).

While stations GAS and VES are far from tide-water glaciers, at HBK glacier ice from Hansbreen calving may contribute to wave attenuation by drifting glacier ice and to shore protection by ice pushed to the foreshore. The peak of Hornsund glacier calving is August–November (Błaszczyk et al., 2013), the season with generally no sea ice. Swirad et al. (2024) observed a secondary peak in fjord ice coverage around October which they interpreted as the glacier ice. Although most of that ice is related to large glaciers in eastern Hornsund, the peak timing likely represents Hansbreen as well. It may be important as winter storms start rolling into the fjord in autumn (Wojtysiak et al., 2018) and glacier ice may buffer beaches from wave attack. Ice from Hansbreen calving accumulates not only along Hansbukta, but also Isbjørnhamna shores, where the Polish Polar Station infrastructure is located—notably the boathouse and petrol tanks (Zagórski et al., 2015). Little is known, however, of the protective role of glacier ice accumulated at the shores, particularly in quantitative terms. Similarly, little research has been done on the protective role of ice foot at the beach, though, when present, it may completely protect the shore from wave attack (Rodzik and Zagórski, 2009). By providing boundary conditions necessary for analyses focusing on the nearshore zone, our study is an important prerequisite to answering these questions and to more reliably assessing the vulnerability of Hornsund’s coasts to the changing wave and ice climate.

Data accessibility statement

The SWAN model is freely available at https://swanmodel.sourceforge.io/. The NCEP GFS wind data (National Centers for Environmental Prediction, 2015) are available at https://doi.org/10.5065/D65D8PWK. The wave energy spectra from Arctic Ocean Wave Hindcast (2024) are available at https://doi.org/10.48670/moi-00008. The ERA5 data (Hersbach et al., 2023) are available at https://doi.org/10.24381/cds.adbb2d47. The Arctic Ocean Sea Ice Concentration Charts for Svalbard and Greenland (MetNo, 2023) are available through the EU Copernicus Marine Service at https://doi.org/10.48670/moi-00128. The SWAN results for the stations VES, GAS, and HBK are available at https://doi.org/10.5281/zenodo.13871928 (Herman et al., 2024). Full modeling results (over 1TB of data in total) can be obtained from the authors upon request.

Supplemental files

The supplemental files for this article can be found as follows:

Table S1. Text S1–S2. (PDF)

Acknowledgments

All simulations described in this article were carried out at the Academic Computer Centre (TASK) in Gdańsk, Poland. This study utilizes data from the Monitoring System of the Polish Polar Station Hornsund, run by the Institute of Geophysics Polish Academy of Sciences and financed by the Polish Ministry of Science and Higher Education.

Funding

This work has been financed by Polish National Science Centre project no. 2021/40/C/ST10/00146.

Competing interests

The authors have declared that no competing interests exist.

Author contributions

Contributed to conception and design: AH, ZMS, MM.

Contributed to acquisition of data: MM, ZMS.

Configured and ran the model, processed modeling results: AH.

Contributed to analysis and interpretation of the results: AH, ZMS, MM.

Drafted the article: AH.

Revised the article and approved the submitted version for publication: AH, ZMS, MM.

References

Arctic Ocean Wave Hindcast. 2024. E.U. Copernicus Marine Service Information (CMEMS). Marine Data Store (MDS). DOI: https://doi.org/10.48670/moi-00008.

Arntsen, M, Sundfjord, A, Skogseth, R, Błaszczyk, M, Promińska, A.2019. Inflow of warm water to the inner Hornsund fjord, Svalbard: Exchange mechanisms and influence on local sea ice cover and glacier front melting. Journal of Geophysical Research: Oceans124(3): 1915–1931. DOI: http://dx.doi.org/10.1029/2018JC014315.

Atkinson, DE. 2005. Observed storminess patterns and trends in the circum-Arctic coastal regime. Geo-Marine Letters25(2–3): 98–109. DOI: https://doi.org/10.1007/s00367-004-0191-0.

Barnhart, KR, Miller, CR, Overeem, I, Kay, JE.2016. Mapping the future expansion of Arctic open water. Nature Climate Change6: 280–285. DOI: http://dx.doi.org/10.1038/nclimate2848.

Barnhart, KR, Overeem, I, Anderson, RS.2014. The effect of changing sea ice on the physical vulnerability of Arctic coasts. The Cryosphere8(5): 1777–1799. DOI: http://dx.doi.org/10.5194/tc-8-1777-2014.

Barton, BI, Lenn, Y-D, Lique, C.2018. Observed Atlantification of the Barents Sea causes the polar front to limit the expansion of winter sea ice. Journal of Physical Oceanography48(8): 1849–1866. DOI: http://dx.doi.org/10.1175/JPO-D-18-0003.1.

Bertin, X, Prouteau, E, Letetrel, C.2013. A significant increase in wave height in the North Atlantic Ocean over the 20th century. Global and Planetary Change106(3–4): 77–83. DOI: http://dx.doi.org/10.1016/j.gloplacha.2013.03.009.

Błaszczyk, M, Jania, JA, Kolondra, L.2013. Fluctuations of tidewater glaciers in Hornsund fjord (southern Svalbard) since the beginning of the 20th century. Polish Polar Research34(4): 327–352.

Casas-Prat, M, Wang, XL.2020. Projections of extreme ocean waves in the Arctic and potential implications for coastal inundation and erosion. Journal of Geophysical Research: Oceans125(8): e2019JC015745. DOI: http://dx.doi.org/10.1029/2019JC015745.

Dumont, D. 2022. Marginal ice zone dynamics: History, definitions and research perspectives. Philosophical Transactions of the Royal Society A380(2235): 20210253. DOI: http://dx.doi.org/10.1098/rsta.2021.0253.

Gerland, S, Ingvaldsen, RB, Reigstad, M, Sundfjord, A, Bogstad, B, Chierici, M, Hop, H, Renaud, PE, Smedsrud, LH, Stige, LC, Arthun, M, Berge, J, Bluhm, BA, Borgå, K, Bratbak, G, Divine, DV, Eldevik, T, Eriksen, E, Fer, I, Fransson, A, Gradinger, R, Granskog, MA, Haug, T, Husum, K, Johnsen, G, Jonassen, MO, Jørgensen, LL, Kristiansen, S, Larsen, A, Lien, VS, Lind, S, Lindstrøm, U, Mauritzen, C, Melsom, A, Mernild, SH, Muller, M, Nilsen, F, Primicerio, R, Søreide, JE, van der Meeren, GI, Wassmann, P.2023. Still Arctic?—The changing Barents Sea. Elementa: Science of the Anthropocene11(1): 00088. DOI: http://dx.doi.org/10.1525/elementa.2022.00088.

Gomes da Silva, P, Coco, G, Garnier, R, Klein, AHF.2020. On the prediction of runup, setup and swash on beaches. Earth-Science Reviews204: 103148. DOI: http://dx.doi.org/10.1016/j.earscirev.2020.103148.

Harley, MD, Turner, IL, Kinsela, MA, Middleton, JH, Mumford, PJ, Splinter, KD, Phillips, MS, Simmons, JA, Hanslow, DJ, Short, AD.2017. Extreme coastal erosion enhanced by anomalous extratropical storm wave direction. Scientific Reports7(1): 6033. DOI: http://dx.doi.org/10.1038/s41598-017-05792-1.

Herman, A, Swirad, Z, Moskalik, M.2024. SWAN wave model simulations for Hornsund, Svalbard, 07.2015-06.2023 [Data set]. Zenodo. DOI: https://doi.org/10.5281/zenodo.13871928.

Herman, A, Wojtysiak, K, Moskalik, M.2019. Wind wave variability in Hornsund fjord, west Spitsbergen. Estuarine, Coastal and Shelf Science217: 96–109. DOI: http://dx.doi.org/10.1016/j.ecss.2018.11.001.

Hersbach, H, Bell, B, Berrisford, P, Biavati, G, Horányi, A, Muñoz Sabater, J, Nicolas, J, Peubey, C, Radu, R, Rozum, I, Schepers, D, Simmons, A, Soci, C, Dee, D, Thépaut, J-N.2023. ERA5 hourly data on single levels from 1940 to present. Copernicus Climate Change Service (C3S) Climate Data Store (CDS). DOI: https://doi.org/10.24381/cds.adbb2d47. Accessed July 30, 2024.

Holthuijsen, LH. 2007. Waves in oceanic and coastal waters. Cambridge University Press: 387. DOI: http://dx.doi.org/10.1017/CBO9780511618536.

Irrgang, AM, Bendixen, M, Farquharson, LM, Baranskaya, AV, Erikson, LH, Gibbs, AE, Ogorodov, SA, Overduin, PP, Lantuit, H, Grigoriev, MN, Jones, BM.2022. Drivers, dynamics and impacts of changing Arctic coasts. Nature Reviews Earth and Environment3: 39–54. DOI: http://dx.doi.org/10.1038/s43017-021-00232-1.

Jakacki, J, Przyborska, A, Kosecki, S, Sundfjord, A, Albretsen, J.2017. Modelling of the Svalbard fjord Hornsund. Oceanologia59(4): 473–495. DOI: http://dx.doi.org/10.1016/j.oceano.2017.04.004.

Jiang, X, Gao, D, Hua, F, Yang, Y, Wang, Z.2022. An improved approach to wave energy resource characterization for sea states with multiple wave systems. Journal of Marine Science and Engineering10(10): 1362. DOI: http://dx.doi.org/10.3390/jmse10101362.

Kowalik, Z, Marchenko, A, Brazhnikov, D, Marchenko, N.2015. Tidal currents in the western Svalbard fjords. Oceanologia57(4): 318–327. DOI: http://dx.doi.org/10.1016/j.oceano.2015.06.003.

Lind, S, Ingvaldsen, RB, Furevik, T.2018. Arctic warming hotspot in the northern Barents Sea linked to declining sea-ice import. Nature Climate Change8(7): 634–639. DOI: http://dx.doi.org/10.1038/s41558-018-0205-y.

Mentaschi, L, Vousdoukas, MI, Voukouvalas, E, Dosio, A, Feyen, L.2017. Global changes of extreme coastal wave energy fluxes triggered by intensified teleconnection patterns. Geophysical Research Letters44(5): 2416–2426. DOI: http://dx.doi.org/10.1002/2016GL072488.

MetNo. 2023. Arctic ocean sea ice concentration charts—Svalbard and Greenland. E.U. Copernicus Marine Service Information (CMEMS). Marine Data Store (MDS). DOI: https://doi.org/10.48670/moi-00128. Accessed September 30, 2024.

Muckenhuber, S, Nilsen, F, Korosov, A, Sandven, S.2016. Sea ice cover in Isfjorden and Hornsund, Svalbard (2000–2014) from remote sensing data. The Cryosphere10(1): 149–158. DOI: http://dx.doi.org/10.5194/tc-10-149-2016.

National Centers for Environmental Prediction. 2015. NCEP GFS 0.25 degree global forecast grids historical archive. DOI: https://doi.org/10.5065/D65D8PWK.

Nielsen, DM, Pieper, P, Barkhordarian, A, Overduin, P, Ilyina, T, Brovkin, V, Baehr, J, Dobrynin, M.2022. Increase in Arctic coastal erosion and its sensitivity to warming in the twenty-first century. Nature Climate Change12(3): 263–270. DOI: http://dx.doi.org/10.1038/s41558-022-01281-0.

Onarheim, IH, Årthun, M.2017. Toward an ice-free Barents Sea. Geophysical Research Letters44(16): 8387–8395. DOI: http://dx.doi.org/10.1002/2017GL074304.

Onarheim, IH, Årthun, M, Teigen, SH, Eik, KJ, Steele, M.2024. Recent thickening of the Barents Sea ice cover. Geophysical Research Letters51(10): e2024GL108225. DOI: http://dx.doi.org/10.1029/2024GL108225.

Osuch, M, Wawrzyniak, T.2016. Climate projections in the Hornsund area, Southern Spitsbergen. Polish Polar Research37: 379–402.

Padman, L, Erofeeva, S.2004. A barotropic inverse tidal model for the Arctic Ocean. Geophysical Research Letters31(2): L02303. DOI: http://dx.doi.org/10.1029/2003GL019003.

Polyakov, IV, Pnyushkov, AV, Alkire, MB, Ashik, IM, Baumann, TM, Carmack, EC, Goszczko, I, Guthrie, J, Ivanov, VV, Kanzow, T, Krishfield, R, Kwok, R, Sundfjord, A, Morison, J, Rember, R, Yulin, A.2017. Greater role for Atlantic inflows on sea-ice loss in the Eurasian Basin of the Arctic Ocean. Science356(6335): 285–291. DOI: http://dx.doi.org/10.1126/science.aai8204.

Rodzik, J, Zagórski, P.2009. Shore ice and its influence on development of the shores of southwestern Spitsbergen. Oceanological and Hydrobiological Studies38(1): 163–180.

Schlichtholz, P. 2021. Relationships between wintertime sea ice cover in the Barents Sea and ocean temperature anomalies in the era of satellite observations. Journal of Climate34(5): 1565–1586. DOI: http://dx.doi.org/10.1175/JCLI-D-20-0022.1.

Semedo, A, Vettor, R, Breivik, Ø, Sterl, A, Reistad, M, Soares, CG, Lima, D.2015. The wind sea and swell waves climate in the Nordic seas. Ocean Dynamics65(2): 223–240. DOI: http://dx.doi.org/10.1007/s10236-014-0788-4.

Siew, PYF, Wu, Y, Ting, M, Zheng, C, Ding, Q, Seager, R.2024. Significant contribution of internal variability to recent Barents–Kara sea ice loss in winter. Communications Earth and Environment5(1): 411. DOI: http://dx.doi.org/10.1038/s43247-024-01582-6.

Squire, VA. 2018. A fresh look at how ocean waves and sea ice interact. Philosophical Transactions of the Royal Society A376(2129): 20170342. DOI: http://dx.doi.org/10.1098/rsta.2017.0342.

Stopa, JE, Ardhuin, F, Girard-Ardhuin, F.2016. Wave climate in the Arctic 1992–2014: Seasonality and trends. The Cryosphere10(4): 1605–1629. DOI: http://dx.doi.org/10.5194/tc-10-1605-2016.

Sumata, H, de Steur, L, Divine, DV, Granskog, MA, Gerland, S.2023. Regime shift in Arctic Ocean sea ice thickness. Nature615(7952): 443–449. DOI: http://dx.doi.org/10.1038/s41586-022-05686-x.

SWAN Team. 2024. SWAN Cycle III, version 41.45, scientific and technical documentation. Technical Report. Delft University of Technology, Faculty of Civil Engineering and Geosciences. Available athttps://swanmodel.sourceforge.io/. Accessed May 5, 2025.

Swirad, ZM, Johansson, AM, Malnes, E.2024. Extent, duration and timing of the sea ice cover in Hornsund, Svalbard, from 2014–2023. The Cryosphere18(2): 895–910. DOI: http://dx.doi.org/10.5194/tc-18-895-2024.

Swirad, ZM, Moskalik, M, Herman, A.2023. Wind wave and water level dataset for Hornsund, Svalbard (2013–2021). Earth Systems Science Data15(6): 2623–2633. DOI: http://dx.doi.org/10.5194/essd-15-2623-2023.

Thomson, J. 2022. Wave propagation in the marginal ice zone: Connections and feedback mechanisms within the air–ice–ocean system. Philosophical Transactions of the Royal Society A380(2235): 20210251. DOI: http://dx.doi.org/10.1098/rsta.2021.0251.

Urbański, JA, Litwicka, D.2022. The decline of Svalbard land-fast sea ice extent as a result of climate change. Oceanologia64(3): 535–545. DOI: http://dx.doi.org/10.1016/j.oceano.2022.03.008.

Wojtysiak, K, Herman, A, Moskalik, M.2018. Wind wave climate of west Spitsbergen: Seasonal variability and extreme events. Oceanologia60(3): 331–343. DOI: http://dx.doi.org/10.1016/j.oceano.2018.01.002.

Zagórski, P, Rodzik, J, Moskalik, M, Strzelecki, MC, Lim, M, Błaszczyk, M, Promińska, A, Kruszewski, G, Styszyńska, A, Malczewski, A.2015. Multidecadal (1960–2011) shoreline changes in Isbjørnhamna (Hornsund, Svalbard). Polish Polar Research36(4): 369–390.

Zhou, W, Leung, LR, Lu, J.2024. Steady threefold Arctic amplification of externally forced warming masked by natural variability. Nature Geoscience17(6): 508–515. DOI: http://dx.doi.org/10.1038/s41561-024-01441-1.