In the Baltic Sea, the variations of sea level (SL) are controlled by meteorological and climatological processes, including the hydrological balance (Johansson et al., 2001). Tides give a small contribution to these variations, since the Scandinavian basins are characterized by low tidal levels during the year. As suggested by Ekman (2009), the Baltic Sea has no real tides, but storm winds could raise the sea level locally by more than 2.4 m. The largest amplitudes reach up to 3–4 m as storm surges and seiches in the Gulf of Finland (Kulikov et al., 2014). In general, the tide is a few centimetres high, with peaks of about 24 cm in the Gulf of Finland, as estimated by Medvedev et al. (2016). In Samuelsson and Stigebrandt (1996), the sea level variations are classified as “external” and “internal”: respectively, long-term winds transporting water between the Atlantic Ocean and the Baltic Sea and short-term winds together with changes of density and barometric pressure, redistributing water within the Baltic Sea. Those two types of variability may exhaustively explain the low-frequency SL changes in the Baltic Sea. Being that those changes are predominantly influenced by air pressure and wind stress, the variability is mostly of random character and seasonal cycles are dominant (Kulikov et al., 2014). According to Hünike and Zorita (2005), during the summer, temperature and precipitation explain part of the SL variability except in the Kattegat region. Furthermore, SL exhibits an annual cycle peaking in the winter months.

SL variations are of great importance and have been thoroughly investigated by many researchers, for example, with the purpose of broadening the knowledge on climate change (IPCC, 2018), spatial patterns (Ekman, 1996; Donner et al., 2012), land uplift (Miettinen et al., 1999) and the pole tide (Ekman, 1996; Medvedev et al., 2014) in the Baltic Sea. The reason why the study presented in this paper has been carried out is to give wave energy developers additional information to use when looking for suitable sites for their devices. Generically, a wave energy converter (WEC) extracts energy from high-frequency waves, while it might be negatively affected by low-frequency SL changes depending on its design. The Uppsala WEC, shown in Fig. 1, is considered as an example. The WEC consists of a surface-floating buoy vertically driving an encapsulated linear generator on top of a foundation acting as a fixed reference on the sea floor. The tension in the connection line and the distance between the buoy and the sea bed is influenced by low-frequency SL variations: for a significantly low SL, the connection line is slack and the translator rests on the bottom of the generator, while for a significantly high SL, the translator continuously hits the upper end stop, which results in additional stresses on the hull of the generator and in a reduced stroke of the translator itself. In both cases, the energy absorption decreases drastically, together with the lifetime and survivability of the WEC (Castellucci et al., 2016). The same problem is experienced by other technologies, such as oscillating water columns, as suggested by Muetze and Vining (2006) and by López et al. (2015), and in more general terms by WECs which have a part that is fixed in position relative to the sea bed and a part that moves with the waves. Well-known point absorbers, such as Carnegie CETO (Kenny, 2014), Ocean Power Technologies Powerbuoy (OPT, 2018) and Archimedes Wave Swing (Beirdol et al., 2007), are challenged by SL changes, either because of a limited stroke length or because of the exponential decrease in available energy with depth.

The work presented in this paper is part of a bigger wave energy project on Swedish wave energy resource mapping (SWERM) financed by the Swedish Energy Agency (Strömstedt et al., 2017). The project aims to generate and combine different layers of information, like bathymetry, sea ice coverage, wave climate, wave energy conversion potential, etc. for the Swedish Exclusive Economic Zone (SEEZ) in order to identify the most suitable areas for wave energy conversion. Within this framework, the study here conducted aims to evaluate the SL information layers: the paper presents the results for the SL variations over a larger area that includes the SEEZ and adjacent seawaters (see Fig. 2). The input data and the methodology are discussed in Sect. 2. The results are shown in Sect. 3 by means of maps. Geographic Information System (GIS) layers will be available online or upon request at the end of the project, so that detailed data can be extracted. Finally, the discussion and conclusion are presented in Sects. 4 and 5.

In order to produce comprehensive maps of sea surface height (SSH) in the Baltic Sea as a whole, it is necessary to interpolate the available data over space and time. However, measurement stations are located far from each other, even more than 100 km, and some are visited only once a month. Some may lack observations for very long time periods. In order to compensate for those deficiencies, observations are combined with model simulations to obtain a homogeneous data set with high resolution in time and space, and reasonably close to observations. This can be achieved with a process called data assimilation, in which observations are used to update the circulation model to keep it from deviating too far away from reality (Axell and Liu, 2016).

The circulation model used by the Swedish Meteorological and Hydrological Institute (SMHI) to produce the reanalysis data used in this study is HIROMB (High-Resolution Operational Model for the Baltic). HIROMB has open boundaries in the western English Channel and in the northern North Sea. For SSH, HIROMB uses data from the coarse storm-surge model NOAMOD (44 km resolution), whereas climatological monthly mean values are used for salinity and temperature. Moreover, ice variables are assumed to be zero at the boundary. The meteorological forcing is from the High-Resolution Limited Area Model (HIRLAM, 2019), with a resolution of 22 to 11 km. The chosen data assimilation method is the 3DEnVar (3-D ensemble variational) data assimilation, a multivariate method where many variables are affected by each observation. The observations assimilated into this model are ice concentration, level ice thickness, sea surface temperature and profiles of salinity and temperature. The directly affected model variables are the same, i.e. ice concentration, level ice thickness, salinity and temperature. Other variables are affected indirectly to a small degree, including, e.g. currents and SSH (through its effects on density). However, the differences in currents and SSH compared to a free run without data assimilation are rather small. For more information regarding the model description and validation, see Axell and Liu (2016) and the product documentation (Copernicus, 2018). In general, the results obtained for SSH in the SEEZ and the adjacent seawaters are rather good: mean correlations of about 0.91 and mean root mean square (rms) errors of about 9 cm are calculated by comparing hourly instantaneous model data with corresponding coastal observations for three different years. The SSH data available online at http://marine.copernicus.eu (last access: 18 April 2018) have a spatial resolution of 1/20∘ in the north–south direction and 1/12∘ in the east–west direction, which translates into about 5.5 km resolution. The requirement set by the SWERM project is to work on a common grid of about 1 km2; hence, the reanalysis data have been linearly interpolated with the purpose of fitting this grid. Moreover, a 10-year data set (2007 to 2016) with a temporal resolution of 1 h has been chosen in order to examine the annual and monthly variability of the SSH1h oscillations, neglecting extreme events. Within this study, the terms SL and SSH are generally interchangeable, while SSH1h refers more strictly to the data used to carry out the analysis. Figure 3 shows an excerpt of the simulated model data from January 2014 to December 2015 at two representative locations: Väderöarna and Landsort, in the Skagerrak (latitude: 58.5760, longitude: 11.0661) and in the northwestern Gotland Basin (latitude: 58.7404, longitude: 17.8655), respectively.

The metrics considered relevant to this study are the maximum range and the standard deviation of the SL variations. Note that both metrics are independent of the choice of reference level. The range, calculated as the difference between the highest SSH1h and the lowest SSH1h during the selected time period, gives an indication of the maximum variation of the SL. Some WEC technologies may be unaffected by variations below a certain range, like the Uppsala WEC in mild wave climates, as discussed in Sect. 4. Furthermore, the highest absorption loss for a device can be estimated by WEC developers as presented in the case study in Sect. 3, and mitigation measures can be adopted. The standard deviation (SD), calculated as the square root of the variance for the chosen data set, quantifies the dispersion of the data from their mean value. The higher the SD, the more spread out the data points are from the expected value; hence, it is a measure of the variability of the SL variations. When selecting a site for WEC deployment, one may find it preferable to choose an area with as constant conditions as possible: the frequency of occurrence of high ranges is greater for higher values of SD and the design costs for a WEC may increase with it. In general, the lower the standard deviation, the better it is. Moreover, both metrics, range and SD, are independent of the choice of reference level, which for SL is not always self-evident (Johansson et al., 2001). In fact, the data set provided by Copernicus have a zero mean value at the outer boundary, in the Atlantic. In the Baltic Sea, the SL is higher due to the density difference between the Atlantic Ocean and the Baltic Sea.

The SL range is calculated in Eqs. (1) and (2) as the difference between the absolute maximum and minimum values over the 10-year data set of SSH1h, denoted as MSSHR10y, and over 10 years per each month, denoted as MSSHRm,10y. In other words, 1MSSHR10y=max⁡SSH1h,i-min⁡SSH1h,i2MSSHRm,10y=max⁡(SSH1h,m|10y)-min⁡(SSH1h,m|10y), where i=1,2…N with N being the number of all the SSH1h in the 10-year data set, and m corresponds to the month of the year.

The SD has been obtained, using Eqs. (3)–(6), as the average of annual SDs over the 10-year data set, SD10y, and as the square root of the pooled variance to aggregate monthly SD over 10 years, SDm,10y. More specifically, 3SDm,y=1nm,y-1∑j=1nm,ySSH1h,j-SSH1h,j‾24SDy=∑m=112nm,y-1SDm,y2∑m=112nm,y-1=n1,y-1SD1,y2+n2,y-1SD2,y2+…+n12,y-1SD12,y2(n1,y-1)+(n2,y-1)+…+(n12,y-1)5SDm,10y=110∑y=110SDm,y6SD10y=110∑y=110SDy, where j=1,2,…nm,y, with nm,y equal to the number of SSH1h in a month (m) for the year (y), which may vary depending on the month and year, for the entire 10-year data set. The pooled variance in Eq. (4) is weighted taking into consideration that every month has a different number of days and hence number of SSH1h values.

Finally, a case study is presented in order to give an idea of how the results can be used by wave energy developers. The Uppsala WEC technology is considered. In particular, the energy absorption of an L12 generator is simulated by hydrodynamic modelling. The following features are assumed: a cylindrical buoy of radius 3 m and draft 0.6 m; a translator stroke length of about 2.5 m; a total weight of the moving parts except the buoy of 10 t; a damping factor of about 135 kNs m-1. For more details regarding the model and its limitations, see Castellucci et al. (2016). For the mere purpose of providing an example of WEC energy absorption at different SLs, a sea state characterized by a significant wave height (Hs=1 m) and energy period (Te=5 s) is used as input to the model. These values are considered to be a reasonable approximation of the wave climate in the Baltic Sea (Soomere and Zaitseva, 2007; Soomere et al., 2012; Zaitseva, 2013).

The results for SL range and SD are summarized in Sect. 3.1.1 and 3.1.2, respectively. The energy absorption as a function of the SL for an Uppsala WEC is estimated for a specific sea state and presented in Sect. 3.2.

When designing WECs and choosing suitable sites for wave parks deployment, one generally has to consider wave power potential, water depth and sea bed profile, distance to shore, accessibility and permissions, ice concentration, SL variations, etc. which are all studied in the SWERM project for the SEEZ. This paper gives an overview of the SL variations in the SEEZ and adjacent seawaters by means of the maps presented in Sect. 3. The same methodology described in Sect. 2 can be used to produce SL information layers (GIS layers) for other regions than the Baltic Sea.

As discussed, among others, by Johansson et al. (2001), Ekman (1996) and Stramska et al. (2013), the variability at a specific location of the Baltic Sea shows no apparent trend on a short timescale (10 d to 3 months), while it does on a seasonal timescale, when significantly higher variations in winter compared to summertime are observed. Moreover, they argue that the spatial behaviour of the SD is clear on both interannual and seasonal timescales and it follows a specific pattern. These findings are in strong agreement with the results presented in this paper (see Figs. 6 and 7).

The highest decadal ranges presented in Fig. 5 show that the range of oscillations increases as we move out from the northwestern Gotland Basin (min. value =1.2 m) to the Bothnian Bay, the Danish straits and the Gulf of Finland (max. value =4.3 m). The monthly ranges shown in Fig. 4 confirm the same spatial pattern and an unsurprising seasonal tendency: the range is lower during summertime and higher during wintertime; in particular, July is the mildest month and January the one with the highest ranges.

The SD of the SSH1h confirms the same spatial and temporal patterns. Based on the SDm,10y (see Fig. 6), the most pronounced variability appears to occur during the wintertime (November–January), while the summertime (May–July) is the one with the smallest variability. In general, the values of SD are quite large if compared with the rest of the globe, meaning that the variability of the SSH1h is rather big. This has been shown as well by Ducet et al. (2000) in Plate 1 and by Thompson and Demiro (2016) in their Fig. 3. With reference to Fig. 7 in this study, the lowest SD10y values are found in the Bothnian Sea, Åland and Archipelago seas, Gotland basins, characterized by SD10y≤0.1 m.

Note that a gap in the SSH1h data set has been identified during a few days in February 2008 and from 24 February to 10 March 2012. This does not influence the results in a drastic way, considering that February and March are not the most critical months and that the missing data points are a small percentage (∼0.5 %) of the total analysed data set. Regarding the peaks of SSH1h that are important when calculating the maximum ranges, the reanalysis model of SMHI tends to underestimate them. However, the correlation between model and observations is 0.91, and the rms error is 9 cm for the Baltic Sea (Copernicus, 2018). An educated guess by SMHI would be that the underestimation is about 10 %. In general, the model responds correctly to changes in air pressure, winds, tides and so on. The fluctuations of SL caused by barotropic saltwater inflow events are captured by the model but do not drastically affect the maximum range. As an example, the major Baltic inflow event of December 2014 (Mohrholz, 2018) did not significantly influence the results in either the Skagerrak or the central Baltic Sea, as illustrated in Fig. 3. In fact, as suggested by Mohrholz (2018), the majority of large inflow events are related to sea level changes between 30 and 60 cm. In general, analysing the origins of the MSSHR was not in the scope of the study. Further investigation can be conducted as future work.

As mentioned before, low-frequency changes in SL may affect the performance of WECs. The case study presented in this paper aims to give an idea of the magnitude of the problem and to provide an example for WEC developers. A specific point absorber, the Uppsala WEC, and a representative annual average significant wave height (Hs) of 1 m are here considered. The first assumption limits the validity of the results for other devices: the energy absorption as a function of the SL variation (Fig. 8) should be carefully simulated or measured case by case. The second assumption reduces the scatter diagram of the sea state occurrences to one average state at an unspecified site: a WEC developer should select the most suitable sites on the basis of, e.g. the accessibility and the wave power resource, then calculate the energy output for different sea states and aggregate the results in order to narrow down the number of suitable sites.

For the examined case, the areas where the WEC energy absorption is unaffected by the changes in SL are part of the Gotland basins and a limited area of the Bothnian Sea, where the MSSHR10y is contained in the interval 1.15–1.55 m (see Fig. 11). If a more detailed analysis would be carried out, considering, e.g. the full scatter diagram of sea states at each site, then the basins highlighted in Fig. 11 would certainly be different. Moreover, solutions for mitigating the negative effect of SL variations may be considered, e.g. the stroke length of the Uppsala WEC could be extended by applying changes in the design of the generator, or a compensation system to regulate the length of the connection line could be included in the design of the converter (Castellucci et al., 2016). Integrating a solution into the WEC design would increase the number of sites for wave park deployment but most likely at higher capital investment cost.

Finally, it should be mentioned that according to the wave power technology one wants to investigate, a more detailed analysis of the frequency of occurrence of high ranges at a chosen site could be useful. This choice is dictated by the requirements set by every specific wave energy technology.

The dependency of the energy absorption on the low-frequency SL variation for wave energy converters is a matter of interest for different WEC technologies. For this reason, the changes in SL in the SEEZ and adjacent seawaters have been investigated in the frame of the SWERM project. The study carried out in this paper aims to give a deeper understanding of the variability of the SL in those basins and to provide an information layer (GIS layer) that, once the SWERM project will be completed, will be combined with other layers of information (GIS layers) to suggest suitable sites for wave park deployment. From the calculation of the SSH1h standard deviation, it is clear that the variations of the high-frequency oscillations during the latest decade are limited especially in the Bothnian Sea, Åland and Archipelago seas, and Gotland basins, where SD10y≤0.1 m. The maximum range of these variations increases as we move out from the northwestern Gotland Basin to the Bothnian Bay, the Danish straits and the Gulf of Finland. The MSSHR10y varies from the lowest value of 1.2 m (northwestern Gotland Basin) to the maximum value of 4.3 (Gulf of Finland) during the period 2007–2016. The seasonal variability is evident: it is more pronounced during the wintertime and less during the summertime. The spatial variability is also noticeable and almost independent of the month: the highest oscillations are found in the Bothnian Bay, the Gulf of Finland, the Kattegat and in the Danish straits, reaching up to 4 m in the Gulf of Finland. More constant conditions are found in the northwestern Gotland Basin, characterized by MSSHR10y of 1.2 to 1.5 m, with very low range during summertime (<0.7 m).

With the purpose of comprehending how the SL can affect a point absorber WEC, an example has been shown. An Uppsala WEC with specified features has been considered and the energy absorption as a function of the SL has been evaluated, assuming a wave climate of relevance for wave energy conversion with a high rate of occurrence in the SEEZ and adjacent seawaters. From a MSSHR10y point of view, areas suitable for deployment are found in the Bothnian Sea, northwestern and eastern Gotland basins, where the 10-year maximum range is contained in the interval 1.15–1.55 m.