Wind wave and water level dataset for Hornsund, Svalbard (2013-2021)

. Underwater pressure sensors were deployed near-continuously at various locations of the nearshore (8  23 m depth) Hornsund fjord, Svalbard between July 2013 and February 2021. Raw pressure measurements at 1 Hz were used to derive mean water levels, wave spectra and bulk wave parameters for 1024 s bursts at hourly intervals. The procedure included 10 subtracting atmospheric pressure, depth calculation, Fast Fourier Transform, correction for the decrease of the wave orbital motion with depth and adding a high-frequency tail. The dataset adds to the sparse in situ measurements of wind waves and water levels in the Arctic, and can be used e.g. for analysing seasonal wind wave conditions and inter-annual trends, and calibrating/validating wave models.


Introduction 15
In situ wave measurements are critical for understanding wave climate, analysing seasonal and inter-annual trends, and calibrating and validating wave transformation models (e.g. Reistad et al., 2011). Spatial distribution of instruments providing wind wave data is irregular and tends to concentrate in mid-and low-latitude coastal areas (e.g. https://www.ndbc.noaa.gov/; Semedo et al., 2015). In the Arctic, the network of such instruments is particularly sparse. There is a pertinent lack of continuous wave data in the Svalbard archipelago where communities, industry infrastructure, and research stations are located. 20 Continuous wave observations in the coastal Arctic are needed to better understand how i) decreasing sea-ice extentpan-Arctic annual mean extent decrease of 3.5-4.1% per decade (IPCC, 2019) or 1.5 to 3-fold increase of the length of sea-ice free season along pan-Arctic coasts (Barnhart et al., 2014(Barnhart et al., ) between 1979(Barnhart et al., and 2012 increasing frequency and strength of storms (Francis et al., 2011;Wang et al., 2015;Stopa et al., 2016;Waseda et al., 2018), and, in consequence, iii) higher waves acting on Arctic coasts for longer time periods contribute to coastal flooding and erosion, that can cause infrastructure damage 25 (Forbes, 2011).
The large-scale models are good for understanding the general trends in the Arctic/Svalbard area, but provide limited information on local-scale wave parameters in specific fjords and bays (Nederhoff et al., 2022). How the open ocean wave conditions translate into wave conditions in the coastal areas is poorly constrained given complex coastal wind patterns and bottom topography (Semedo et al., 2015). Moreover, the large-scale models over-simplify most aspects of wind wave-sea ice 45 interactions. Most operational models use simple empirical formulae for wave attenuation in sea ice (Barnhart et al., 2014;Zhao et al., 2015;Ardhuin et al., 2016). Herman et al. (2019) used three nested Simulating Waves Nearshore (SWAN; Booij et al., 1999) models to predict wind wave parameters within bays of Hornsund fjord (~15 m depth) taking eastern Greenland Sea WW3 spectra as boundary conditions. 50 They ran the model for two sea-ice free 4-month periods (August -November 2015 and 2016) finding a good agreement between the modelled and measured significant wave height (r 2 > 0.9) and mean absolute wave period (r 2 = 0.630.78). The study added a considerable detail into wind wave transformation in the nearshore environment of Hornsund by including fjord bathymetry, which allowed resolving depth-induced wave breaking and bottom friction on wind conditions. Notably, the study used a subset of the dataset described in this paper to validate the wave spectral model (Herman et al., 2019). 55 The model of Herman et al. (2019) tested against buoy data performed well for ice-free conditions only. For a bay of Beaufort Sea, Nederhoff et al. (2022) incorporated sea ice into SWAN model which enabled to reliably describe wave climate in 19792019. The need for observational data to validate wave models, especially in periods when the sea ice is present, persists. In 19792018 easterly winds dominated at the Polish Polar Station (12 m a.s.l.; PPS in Fig. 1e) with the mean direction of 80 124º (annual mean range of 102-140º). Mean wind speed at ~20 m a.s.l. was 5.5 m s -1 (Wawrzyniak and Osuch, 2020).
Wave conditions in Hornsund are usually related to the long oceanic swell or mixed swell/wind sea from SSW with short wind waves formed locally due to predominantly easterly winds. The mean Hs at the fjord mouth is 1.21.3 m decreasing to 0.50.9 m in the central and to < 0.4 m in the inner parts of Hornsund (Fig. 1c). Northern shores of the fjord receive more 85 wave energy than southern shores (Herman et al., 2019).
Hornsund bays (in this study Hansbukta, Isbjørnhamna, Rettkvalbogen, Veslebogen and Gåshamna) have complex shapes and bottom topography with ubiquitous skerries causing strong wave transformation due to refraction and dissipation (Herman et al., 2019). 90 Sea ice forms locally in the fjord or drifts from the open Greenland Sea. The latter originates east of Svalbard, drifts past the southern tip of Spitsbergen (Sørkapp) and then northwards along the western Spitsbergen coast with cold Sørkapp Current (blue arrow in Fig. 1a). Fast ice (i.e. sea ice attached to the shore) persists during winter months. Muckenhuber et al. (2016) observed a decrease in sea ice (both drift and fast ice) duration and extent between 2000 and 2014. In summer months glacier 95 ice from calving tide-water glaciers (Błaszczyk et al., 2019) may accumulate in bays. Increased storminess coincident with positive air temperature anomalies and the lack of sea ice, in particular in OctoberDecember, may contribute to coastal erosion (Zagórski et al., 2015).

Input data 100
Pressure data were collected between 2013-07-21 and 2021-02-12 using RBR virtuoso P (continuous sampling at 4 or 6 Hz interval), RBR duo TD (continuous sampling at 1 Hz interval) and RBR virtuoso wave (1024 s bursts at 30 min interval with 1 Hz sampling interval or at 60 min interval with 2 Hz sampling interval). There were 24 single deployments with duration of 13599 days (Table 1; Fig. 2). Initially the deployments were short (< 100 days) and usually restricted to the fieldwork season (late spring to autumn). Since 2015, however, deployments were typically ~1-year long with instrument recovery and re-105 deployment during summer field campaigns. As a result of the COVID-19 pandemics, it was impossible to recover instruments in summer 2020, and the last two deployments (GAS5 and VES3) were > 550 days long and ended with the battery death.
The instruments were anchored to the sea bed in various locations in northern (Hansbukta, western and eastern Isbjørnhamna, Rettkvalbogen, Veslebogen) and southern (Gåshamna) Hornsund (Fig. 1d,e). The raw pressure data are part of the 110 LONGHORN oceanographic monitoring of IG PAS and are provided in Swirad et al. (2022).  For consistency the raw data were subsampled to 1024 s bursts at 60 min interval (starting at full hours) with 1 Hz sampling interval. The erroneous bursts at the start and end of deployments were removed. The datasets were cropped to full days so that the first measurement occurs at 00:00:00 UTC (hh:mm:ss) and the last one at 23:17:03 (1024 th s after 11pm). These 24 deployment files are time series with three columns representing time, burst number and raw pressure in dbar, and are available 125 as part of the dataset (Swirad et al., 2023).

Burst processing
The deployment files were imported into Spyder (Python 3.9) and processed on the burst-by-burst basis, with an algorithm described below (see also Wang et al., 1986, Karimpour et al., 2017, Marino et al., 2022. Importantly, 130 all steps described below are based on the linear wave theory; alternative data processing methods (e.g., Bonneton et al., 2018) might be applied to the original burst data to capture nonlinear effects, but they are not considered here.
(4) 145 The slowly-varying component of water depth (due to, e.g., tide and storm surge) was removed by subtracting from a leastsquare-fitted 2 nd order polynomial trend, lf , resulting in time series hf (m), related to depth variability associated with wind waves: hf = − lf . The energy density spectrum at depth , ( ) (in m 2 s), was computed by applying Fast Fourier Transform (FFT; Frigo and Johnson, 2005) to the time series hf . As already mentioned, the data length used for FFT input 150 was 1024. The Python fft function with default settings was used to compute the spectra, and no windowing was applied.
Finally, the spectrum at the sea surface, 0 ( ), was computed from ( ) by applying a correction factor ( ) accounting for the decrease of the wave orbital motion (and thus pressure fluctuations) with depth (compare red and blue spectra in Hz is the minimum frequency used to calculate mean wave parameters, and is the 160 highest frequency reliably measured. The plot is limited to = . Hz which is the upper limit of the observation data. Wave parameters are calculated in two versions, for < < and for < < ∞. To this end, a set of basic wavenumber values was defined, = {0,0.01,0.02, ⋯ ,1000} (m 1 ), and a corresponding set of basic wave frequencies , with elements: 165 The set of correction factors is then given by: = cosh( (ℎ ̅ − lf ̅̅̅))/cosh( ℎ ̅ ), for each ∈ , where ℎ ̅ and lf ̅̅̅ denote the mean bottom depth and the mean logger depth, respectively (in the present case, with loggers 170 mounted at the bottom, ℎ ̅ = lf ̅̅̅; averaging takes place over burst duration). The correction factor in (5) was calculated by linearly interpolating and to the frequencies of the energy spectrum. (Note that in expression (6) was computed from (3, 4) without the last term in (3), i.e., for sea = 0.) As ( ) quickly decreases with increasing wave frequency, the values of 0 ( ) computed from (5) become unreliable for 175 higher than some limiting frequency lastval . Here, lastval was computed for each spectrum separately, based on a universal (constant for all spectra) limiting value of : lim = 0.05 (note that, consistent with the linear wave theory used throughout this analysis, the values of depend only on water depth and frequency of a given spectral component, but not on the amplitude of that component). That is, lastval is the highest frequency for which > lim . For all > lastval , a high-frequency tail of the form 0 ( )~− 4 was added after Kaihatu et al. (2007) by extrapolating the trend from the last = 10 reliably estimated 180 0 ( ) values (yellow line in Fig. 3): where:

Mean wave parameters
In calculation of mean (integral) wave parameters, frequencies < min = 0.04 Hz (corresponding to wave periods higher than 25 s) were ignored. This limit corresponds to the approximate boundary between wind-generated and infragravity waves, as well as to the lower frequency limit typically used in spectral wave models (e.g., Holthuijsen, 2007). Thus, the mean wave parameters were computed for min < < max . In the final dataset, two sets of those parameters are provided, referred to as 190 observational one (for max = lastval ) and modelled one (for max = ∞). The spectral moments of 0 ( ) are defined as: where ̃0 is computed from (9), = 0 if max = lastval and = 1 if max = ∞. Based on , the following wave parameters are calculated: the significant wave height , the mean absolute wave period 0,1 , the mean absolute zero-crossing period 0,2 , and the so-called energy period −1,0 : 195 200

Output data
There are two output files for each deployment with rows representing bursts. The first one ('DepID_properties.txt') contains the information on burst (number and time), mean water depth lf ̅̅̅ , lastval , and the four mean wave parameters defined in Eqs.

Quality control 215
The instruments remained at the sea bed thanks to the anchor weight. However, a few times they were transported by ice or strong waves resulting in an abrupt change in mean depth visible in the output data (e.g. Fig. 5a). This situation occurred three times: in VES1 bursts #83 (depth rise of ~1 m) and #370 (depth drop of ~2.3 m), and in GAS5 burst #13420 (depth rise of ~0.7 m). In the case of VES1 burst #83 and GAS5 burst #13420 it occurred in between bursts with no impact on calculated wave energy spectra and bulk parameters. Therefore, the data are left unchanged. If the dataset is used for tide analysis, 220 timeseries should be split at the depth change event and treated separately. To identify erroneous bursts, we investigated the energy density for < 0.5 Hz and identified two bursts with abnormally high energy density at low frequencies that resulted in erroneous calculation of bulk parameters (e.g. Fig 5b): VES1 burst #370 and HBK1 burst #44. In the first case the error resulted from instrument displacement during the burst. In the second case mean depth rised by ~0.5 m, remained higher for a few hours and droped back to a typical level. There was no anomaly in atmospheric pressure and we speculate that the artefact 225 may be due to a presence of glacier ice at the sea surface. In both cases we replaced all output wave parameters with NaN.

Results
For all bays except Rettkvalbogen timeseries length exceeded one year providing information on seasonal variability in wind 230 wave conditions. The largest waves characterise Veslebogen, a western-most of the analysed northern bays (Fig. 6)

Data availability
The inputs, outputs and the Python code described in this manuscript are available in the PANGAEA repository (https://doi.org/10.1594/PANGAEA.954020; Swirad et al., 2023). Raw data downloaded from the instruments are part of the (https://doi.org/10.25171/InstGeoph_PAS_IGData_NBP_2022_005; Swirad et al., 2022). As the monitoring program is ongoing, future raw and processed in the same way data will be uploaded to the IG PAS Data Portal (https://dataportal.igf.edu.pl/).

Summary
We present the first multi-year continuous wind wave and water level dataset for Hornsund fjord, Svalbard. 24 single 260 deployments of underwater RBR sensors at 823 m depth between July 2013 and February 2021 were used to measure water levels in five bays of northern (Hansbukta, western Isbjørnhamna, eastern Isbjørnhamna, Rettkvalbogen, Veslebogen) and one of southern (Gåshamna) Hornsund. Raw data (Swirad et al., 2022) were subsampled to 1024 s sets (~bursts) at 1 Hz measurement interval at 1 h burst interval that were then used to derive mean water levels, wave spectra and bulk wave parameters. We describe the procedure (available also as a Python code) that includes subtracting atmospheric pressure, depth 265 calculation, Fast Fourier Transform, correction for the decrease of the wave orbital motion with depth and adding a highfrequency tail. We performed quality control on the output data. The dataset can be used to e.g. characterise wind wave climate in Hornsund, identify seasonal to inter-annual trends, calibrate and validate wave models (as shown by Herman et al., 2019), and facilitate e.g. analysis of sea ice impact on wave attenuation, empirical modelling of wave run-up on Arctic beaches and predicting future change. We provide individual bursts with pressure times series and the code for the users to apply different 270 analysis methods, use alternative algorithm parameters, analyse nonlinear effects, etc. depending on the application.
Author contributions. MM initiated and maintains the oceanographic monitoring in Hornsund. ZMS secured the funding.
ZMS wrote the code and processed the data with the support from AH and MM. All authors wrote the manuscript.