Long-term spatial variations in the Baltic Sea wave fields

Introduction Conclusions References


Introduction
Studies into wind wave climate are gaining more importance in the context of global climate change. Surface waves are a major driver of processes in the surface layer of the Correspondence to: T. Soomere (soomere@cs.ioc.ee) entire ocean and especially in the nearshore and coastal areas. The flux of wave energy towards the coasts is responsible for many processes in the nearshore, ranging from longterm accumulation, erosion and degradation that gradually shape the coasts to various marine-induced hazards and disasters. A comprehensive understanding of the properties of the approaching waves and their potential changes is the major knowledge necessary for sustainable management of both offshore activities and the coastal region. Moreover, the wave climate is one of the most sensitive indicators of changes in the wind regime and local climate in semi-enclosed sea areas (Weisse and von Storch, 2010). For example, the potential for the increase in wave heights in the North Sea (18%) is much larger than that of the wind speed (7% for the 99th percentile, Grabemann and Weisse, 2008). Changes in wave climate even in terms of shifts in the stormy season to months with no ice cover may lead to most severe destruction of vulnerable beaches of partially ice-covered seas as has been noticed in the eastern Baltic Sea (Orviku et al., 2003;Ryabchuk et al., 2011).
In this paper we focus on long-term changes and decadal variations in the numerically simulated wave climate in the Baltic Sea. The Baltic Sea is a unique water body, the dynamics of which involves features of a large lake, large estuary and a small ocean (BACC, 2008). The combination of its relatively small size, the vulnerability of its ecosystem and comparatively young coasts makes this region extremely susceptible both to climate changes and anthropogenic pressure (Leppäranta and Myrberg, 2009). As this sea has relatively low overall hydrodynamic activity and is almost nontidal, surface waves play an exceptionally great role in the functioning of the entire environment and especially in the course of coastal processes (Soomere and Healy, 2011). The wave fields in this basin are fully separated from those in the Atlantic Ocean and their changes thus largely represent the changes in the local wave generation conditions. The northern parts of the Baltic Sea freeze over annually. Therefore, ignoring the ice conditions will lead to certain deviations of the resulting wave properties and statistics from the actual one. There is, however, no commonly accepted method to estimate wave statistics in seasonally ice covered domains (Kahma et al., 2003). As our basic goal is to identify (the patterns of) changes that stem from wave generation conditions (that is, the changes that would be evident if there would be no ice cover at all), we choose to consider the hypothetical situation with no ice cover.
Recent research has highlighted greatly variable patterns in the driving factors of the Baltic Sea wind waves . The average wind speed over most of this basin (especially in its southern part) has increased over the last decades (Pryor and Barthelmie, 2003), while a decrease has been documented in the region of the Western Estonian Archipelago and on the southern coast of the Gulf of Finland (Keevallik and Soomere, 2004;Kull, 2005).
The reaction of wave fields to such changes is not obvious and it is not unexpected that the observed changes in the wave properties are quite different in different parts of the Baltic Sea. The annual mean wave heights have increased drastically at both the eastern and western coasts of the northern Baltic Proper (Broman et al., 2006;Soomere and Zaitseva, 2007;Soomere, 2008). The wave activity shows no considerable changes at the Lithuanian coasts (Kelpšaitė et al., 2008) but has decreased substantially at the south-eastern coast of the Gulf of Finland (Narva-Jõesuu, . Another wave field characteristic of similar importance is the wave height in strong storms. The storminess in the entire region gradually decreased over the first half of the 20th century, increased rapidly in the 1980s and 1990s (Alexandersson et al., 1998) and probably decreased again at the very end of the 20th century (Alexandersson et al., 2000;Helminen, 2006). These changes apparently become evident in properties of wind waves. Wave heights in strong storms are usually characterised in terms of the thresholds for 5% and 1% of the highest waves in each calendar year (called the 95th percentile and 99th percentile, respectively). There is implicit evidence about an increase in wave heights in extreme storms  and in those wave conditions that occur together with high water level and cause the most extensive coastal destructions in this microtidal basin (Orviku et al., 2003(Orviku et al., , 2009Tõnisson et al., 2008). Relevant data sets exist only for a selection of sites Suursaar, 2010).
In winter frequent stormy winds and the presence of heavy ice often complicate both visual wave observations and instrumental measurements in the northern Baltic Sea. Floating devices are usually removed well before the ice season (Kahma et al., 2003). As a consequence, the measured wave time series do not contain data from the windiest period that frequently occurs just before the ice cover is formed. Global wave data sets such as KNMI/ERA-40 Wave Atlas (09.1957-08.2002, Sterl and Caires, 2005 have a too coarse spatial resolution (1.5 • × 1.5 • ) for an adequate representation of the Baltic Sea conditions.
We make an attempt to fill this gap by means of highresolution numerical reconstruction of wave properties over almost four decades. Most of similar attempts in the past cover relatively short periods of a few years (Paplińska, 1999(Paplińska, , 2001Jönsson et al., 2002) or concentrate on specific areas (Blomgren et al., 2001;Cieślikiewicz and Herman, 2002;Soomere, , 2005. A few results of longterm reconstructions of wave fields over the entire Baltic Sea have recently been reported in the international literature (Cieślikiewicz and Paplińska-Swerpel, 2008;Kriezi and Broman, 2008). However, as yet no comprehensive description of numerically simulated changes in the wave fields has been presented.
Our study deals with spatial patterns of long-term variations in the basic wave properties such as the annual mean wave height and period, and properties of waves in strong storms. The analysis is based on a numerical reconstruction of the wave fields for 1970-2007 with the use of a high-resolution version (grid step about 3 miles) of the wave model WAM driven by surface-level winds derived from geostrophic wind data. We start from the description of the model setup and definition of the forcing fields. Unlike Martucci et al. (2010), we discuss both the magnitude and the extent of spatial variations in the linear trend in the annual mean and extreme wave heights together with their statistical significance.

Wave model and wind forcing
Wave properties over the entire Baltic Sea (Fig. 1) were computed with the third-generation wave model WAM Cycle 4 (Komen et al., 1994(Komen et al., ) over 38 yr (for 1970(Komen et al., -2007. The implementation of this model for the Baltic Sea conditions takes the following parameters, processes and forcing factors into account: coastal line of the basin, spatial and temporal variation in wind properties, wave propagation on the sea surface, quadruplet interactions between wave harmonics, whitecapping, shoaling and wave dissipation in shallow areas due to bottom friction. This model gives good results in the Baltic Sea if its resolution is appropriate and the wind information is correct (Tuomi et al., 1999;Tuomi, 2008). The triplenested, high-resolution version of the model (with a grid step of about 500 m) has shown good results in several local studies also in quite shallow conditions and adequately represents wave properties up to a depth of about 5 m and as close to the coast as about 200-300 m (Soomere, 2005). As only very few near-coastal grid points in semi-sheltered bays have the model water depth below 5 m and wave heights over 4 m occur with a less than 1% frequency even on the open sea (Kahma et al., 2003;Soomere, 2008), the option of depthinduced breaking is not used. The model output gives at each grid point at chosen times the following parameters: significant wave height, mean wave direction, mean and peak periods, drag coefficient, friction velocity, wind stress fields and two-dimensional (2-D) wave spectrum. In this study we only analyse the wave height and to a limited extent wave periods. The model was run uncoupled from the North Sea wave fields on a grid that was truncated in the narrowest parts of the Danish Straits. The hindcast was performed in shallow-water mode with depth refraction (but without depth-induced breaking) in order to match realistic wave propagation patterns over the highly variable bathymetry of the relatively shallow Baltic Sea.
The bathymetry was based on data by Seifert et al. (2001) and adjusted as described in Soomere (2001). The calculation was undertaken over a regular rectangular grid with a resolution of about 3 × 3 nautical miles. This resolution is somewhat finer than that used in other calculations in the recent past (Jönsson et al., 2002(Jönsson et al., , 2005Cieślikiewicz and Paplińska-Swerpel, 2008;Kriezi and Broman, 2008). The entire grid contains 239 × 208 points (11 545 seapoints) and extends from 09 • 36 E to 30 • 18 E and from 53 • 57 N to 65 • 51 N.
At each seapoint 1008 components (24 equally spaced directions and 42 frequencies from 0.042 Hz (23.9 s) to about 2 Hz (0.5 s) of the 2-D spectrum were computed. The extended frequency range up to 2 Hz was used to ensure realistic wave growth in low wind conditions after calm periods.
Such situations are frequent in the Baltic Sea. The propagation and source time step were both set to 180 s to ensure numerical stability of the integration scheme. The wave properties were recorded hourly for the entire period of calculations.
The central question in the modelling of long-term changes in the wave field is the homogeneity of wind information. Most of high-resolution contemporary wind data sets for the Baltic Sea basin (e.g. MESAN since 1996 (Häggmark et al., 2000) or the wind fields calculated with the local atmospheric models such as HIRLAM) either cover a relatively short time interval or are inhomogeneous in time owing to changes in the numerical scheme. An analysis of the quality of modelled wave fields showed that the quality of wind data obtained from different sources largely varied over the Baltic Sea, whereas the winds derived from the geostrophic wind data showed on average the best performance . Somewhat surprisingly, even high-quality reconstructions of wind fields for two strong storms in this sea in 2001 and 2005, developed by the ECMWF in a 0.25 • ×0.25 • resolution (L. Cavaleri and L. Bertotti, personal communication, 2009), led to the same quality of wave hindcast results as the use of geostrophic winds .
The simulations described below were performed with the use of wind fields constructed on the basis of geostrophic winds. This theoretical wind system represents the equilibrium air flow patterns (an exact balance between the Coriolis effect and the pressure gradient force) corresponding to the large-scale atmospheric pressure patterns. These fields, although they smooth out a large number of local variations in wind properties, are free of local disturbances to the air flow by coastal topography and errors in ground wind speed measurements. The key arguments for their use are that they are highly homogeneous in time and that they represent the impact of global wind patterns which are mostly responsible for the wave climatology.
The geostrophic wind components with a moderate spatial resolution of 1 • ×1 • provided by the Swedish Meteorological and Hydrological Institute (SMHI) were first interpolated to a medium resolution (about 6 nautical miles) grid. The data are available once in 6 h before September 1977 and once in 3 h since then. The geostrophic wind speed was multiplied by 0.6 and the direction turned 15 • anticlockwise to yield an approximation of the wind at the 10 m level.
This approximation, equivalent to one of the options analysed in Bumke and Hasse (1989), is becoming increasingly popular in studies of circulation and wave patterns in the Baltic Sea (Andrejev et al., 2004;Zhurbas et al., 2008;Myrberg et al., 2010) probably because of its simplicity. However, stability questions of the air flow are completely ignored in this approximation. Considerable differences in the properties of air temperature and wind speed compared to the climatology of the Baltic Sea basin for the period 1961-1990 (Mietus, 1998) are reported, for example, for the northern Baltic Sea by Niros et al. (2002). This means that both the ratio of the 10 m level wind speed to the geostrophic wind speed and the angle between the relevant wind vectors may substantially vary in different regions, seasons and wind directions in this basin. The presence of two-peak distributions of strong winds in some parts of the Baltic Proper  may add a certain inaccuracy to the resulting wind field. Also, many Baltic Sea storm patterns exhibit strong ageostrophic features . As the listed distortions of the forcing conditions occur regularly in similar wind situations, their impact on the qualitative appearance of the spatial patterns of long-term changes in wave properties apparently is quite limited.
The resulting wind information was used as the input to the wave model. The wind properties were set constant during the relevant 3 or 6 h time intervals starting from the measurement instant (e.g., the 6 h wind at 12:00 was considered as valid from 12:00 to 18:00). This approach does not affect the long-term statistics but may result in a delay of the properties of the modelled wave fields compared with their measured values. Wind data in a medium resolution (6 miles) were spatially interpolated to the higher resolution wave modelling grid internally in the WAM model.
A detailed description of the performance of the model against instrumental wave measurements and visual wave observations is given in Räämet et al. (2009,  and . The model (i) underestimates to a certain extent wave heights in the range of 0.7-1.5 m but (ii) adequately represents the distribution of the higher waves, (iii) gives qualitatively similar results in terms of short-term variations in the visually observed annual mean wave heights, (iv) provides satisfactory match of the timing and maximum heights in high wave events and (v) reproduces well the overall statistics of wave conditions (incl. the relevant probability distributions) and their seasonal variations.
On average, the model apparently underestimates the longterm average wave height and in many cases failed to reproduce the duration of rough seas. Although this underestimation evidently is connected with the overall low spatial and temporal resolution of the geostrophic wind data because of a non-linear manner of wave growth under varying wind conditions, it is obviously related neither to the change in the time step for the wind data since 1977 nor to the interpolation in time of the wind fields. The underestimation may partially stem from the particular choice of the coefficient (0.6) in the procedure of reduction of the geostrophic winds. This choice was mostly verified by comparison of the measured and modelled wave heights in relatively rough seas (see Figs. 3 and 4 of . A certain bias in the estimates of the long-term magnitude of wave intensity, however, is obviously insignificant in terms of the changes in wave properties described below.

Spatial distributions of long-term wave properties
The basic features of the spatial pattern of numerically simulated average wave heights in the Baltic Sea for 1970-2007 have been discussed by . Therefore we provide here only a short overview of these features. As expected from the properties of predominant winds in the area, the distribution of the long-term average significant wave height (Fig. 2) is asymmetric with respect to the axes of the two largest sub-basins -the Baltic Proper and the Bothnian Sea. The open part of the Bothnian Sea has quite high wave intensity, comparable to that in the northern Baltic Proper. The eastern part of the Bothnian Sea has clearly higher waves (> 0.8 m on average) than its western area.
In the northern Baltic Proper the wave activity is the highest along the coasts of the Western Estonian Archipelago and Latvia. The average wave heights are relatively low along the coasts of Lithuania, Kaliningrad district of Russia and north-eastern Poland. This is somewhat unexpected as these areas have a relatively long fetch. The Gulf of Finland hosts clearly smaller wave activity, with the average wave heights about 0.7 m only at its entrance and in its central part and about 0.6 m in the rest of the gulf, consistently with an estimate for a sea area in the neighbourhood of Tallinn Bay (0.56 m, Soomere, 2005). The largest values of the average wave height only slightly exceed 0.6 m in the Gulf of Riga.
An interesting feature is that the spatial pattern of the areas with large wave activity has several local maxima and The modelled wave periods match well the measured periods: while typical peak periods according to measurements are 4-6 s in the open sea (Soomere, 2008), the average peak periods from simulations are about 4 s. Relative spatial variations in the average periods over the Baltic Sea basin are of the same order of magnitude as similar variations in wave heights. The distributions of periods to some extent match those for the wave height: in both cases they are asymmetric, with the greatest values in the eastern part of the Baltic Proper and the Bothnian Sea. The predomination of southwesterly winds in this area (Mietus, 1998) suggests that the largest wave periods should usually occur in the northern Baltic Proper. The long-term maxima of both peak and mean periods (Fig. 3), however, are found in the southern Baltic Proper. The probable reason for such a location of the peak is that this region has a very long fetch in several directions (especially in the western and N-NW direction) and frequently receives relatively low-frequency swells generated in remote sea areas.

Patterns of long-term changes in average wave properties
The existing evidence about changes in the overall wave intensity is highly controversial and reveals largely different trends in various parts of the Baltic Sea (Broman et al., 2006;Soomere and Zaitseva, 2007;Kelpšaitė et al., 2008;Soomere, 2008). We calculated the relevant trends in the following manner. For each of the 11 545 sea points, first the annual mean significant wave height was calculated from the simulated hourly values. This quantity hereafter is called (overall) wave intensity (or activity). A linear trend was then found for these 38 estimates of the annual wave intensity for each year. The change in the wave height was calculated as the difference between the values for this trendline for the beginning and end years of the simulations. The resulting value of the change is equivalent to a product of the slope of the trendline and the length of the time series. Finally, the statistical significance of the changes for each sea point was found with standard methods in terms of the relevant pvalue. Note that here the significance characterises the match of the annual values of significant wave height with the relevant trendline. Therefore, a high significance indicates that the time series of the annual wave activity can be represented well by a linear model rather than the existence of a significant increase or decrease in the wave height. The simulation reveals a complicated pattern of changes in the wave climate in the Baltic Sea (Fig. 4). The largest changes in the modelled wave activity occur in the southern Baltic Proper. The increase in wave heights in the Arkona basin is consistent with the reported gradual increase in the modelled wind speed over this sea area (Pryor andBarthelmie, 2003, 2010). Surprisingly, the most drastic decrease in wave intensity occurs in a neighbouring area between the islands ofÖland and Gotland, and to the south of these islands down to the Polish coast. The model also suggests a considerable increase in wave activity near the coast of Latvia, between theÅland Archipelago and Sweden, and in the sea area between the Bothnian Sea and the Bothnian Bay. There is also a slight increase in wave activity in both the Gulf of Riga and Gulf of Finland.
Interestingly, the spatial pattern of the described changes is largely uncorrelated with the areas of high and low wave intensity. The area of high waves in the Arkona basin exhibits an increase in wave heights while the wave activity in the neighbouring similar area is decreasing at almost the same rate (about 10 cm, that is, up to 15% in 40 yr). Another area of intense waves near Latvia also reveals an increase in wave heights. The areas subject to significant changes in wave heights to the south and north of the Bothnian Sea host an average wave intensity. Somewhat unexpectedly, the model shows almost no changes for the north-eastern Baltic Proper and along most of the Polish coast.
There is a remarkable match between the areas that show high values of the pointwise calculated statistical significance of the modelled changes (Fig. 5) and the domains that exhibit substantial positive and negative changes in the wave heights (Fig. 4). This match suggests that the wave regime in the five discussed areas has experienced clear changes over the simulation interval. The significance is the highest, about 99%, for the area to the south of Bornholm. The other four areas have typical values of this measure over 90%.
The numerically simulated temporal changes in wave periods (not shown) follow the pattern of changes in wave heights: periods have become longer in the eastern part and shorter in the western part of the Baltic Proper. These changes, however, are quite small, maximally a couple of tenths of seconds and thus can be neglected in practical applications. In other words, the performed calculations suggest that quite substantial variations in long-term wave heights have taken place but no noteworthy increase in the typical wave periods has occurred in the Baltic Sea over the last four decades.

Wave properties in strong storms
Recent research into long-term variations in the largest waves Suursaar, 2010) has shown quite limited changes for selected locations along the Estonian coast. Some results, derived from simple fetch-based wave models and one-point forcing Zaitseva-Pärnaste et al., 2009), indicate a pronounced increase in the 90th percentile and 99th percentile for a location near the coast of the Western Estonian Archipelago, whereas Suursaar (2010) has identified a decrease in the annual mean wave height on the northern coast of Estonia.
The above discussion of the spatial patterns of changes in the overall wave activity suggests that these somewhat controversial results may be caused by an inappropriate choice of the relevant sites. For this reason we studied spatial variations in extreme wave heights based on the simulated values of the 99th percentile and the 95th percentile of significant wave height for each calendar year. As the variations in these two parameters are almost identical, we only present the results for the 99th percentile (Fig. 6), called extreme waves below. These values were calculated over the entire set of hourly wave heights for each year. An estimate of the longterm value of the relevant wave height was then found as an average over the annual values. Finally, the pattern of trends in extreme wave heights and its statistical significance was calculated pointwise similarly to the trends in average wave intensity.
The highest extreme waves occur in the areas with the highest overall wave intensity: in the Arkona basin, south of Gotland, in the north-eastern Baltic Proper and in the eastern Bothnian Sea (Fig. 6a). It is an expected outcome, having the same reasons as those discussed earlier for the average wave heights. Firstly, these areas have the longest fetch. Secondly, the geostrophic winds are relatively strong in the south-eastern part of the Baltic Sea. The changes in extreme wave heights are almost identical to the changes in average wave heights (Fig. 6b). Consistently with the results of Suursaar andSuursaar (2010), a notable decreasing trend in 99th percentiles occurs near the North Estonian coast (which is opposite to a gradual increasing trend in the average wave height) and a slight increase in the heights of extreme waves in the nearshore of the Western Estonian Archipelago.

Conclusions
The described features indicate that certain substantial changes in both average wave intensity (in terms of the annual mean significant wave height) and extreme wave conditions (understood as the wave height occurring with a probability of 1-5%) have occurred over the Baltic Sea since the 1970s. Interestingly, there is a very minor change in the spatially averaged wave height and almost no temporal changes in the wave periods.
However, major changes in both average and extreme wave properties have taken place in different regions. An increase in wave activity in the Arkona basin is not unexpected because the wind speed in this area has grown markedly over the last decades (Pryor andBarthelmie, 2003, 2010). A decrease of the same magnitude in the neighbouring sea area to the north-east of Bornholm is, however, counter-intuitive and further research is necessary to confirm this result of wave modelling. Such a complicated pattern of spatial changes is not completely unexpected as many studies have shown that the magnitudes of the trends in wave properties can greatly vary in different sea areas (Weisse and von Storch, 2010;Martucci et al., 2010, among others). It is, however, notable that a steep decrease in wave heights may occur in open sea areas adjacent to those hosting an equally steep increase in wave heights.
Ironically, most of the wave observation and measurement sites from where long-term data is available (on the eastern coast of the Baltic Sea, on the coasts of the Baltic Proper and in the Gulf of Finland, Fig. 1) are located in areas where the simulations revealed almost no long-term changes in wave properties. We are looking forward to digitising the historical wave data from Latvian coastal observation sites which may confirm the simulated long-term changes.
The wind forcing used in our simulations apparently leads to a certain underestimation of the magnitude of the annual mean wave heights but the values for the higher percentiles of wave conditions are realistic (Räämet et al., 2009). Moreover, it is natural to assume that a large part of long-term changes in wave fields are tightly related to similar changes in the air pressure patterns and the geostrophic winds even in areas where ageostrophic components or specific wave generation conditions (Pettersson et al., 2010) are at times or in places decisive. Therefore, the performed simulations evidently capture realistically the slopes of the relevant trends in wave parameters.
One of the advantages of using the geostrophic wind data is that it implicitly accounts for the presence of ice cover (although the generalized nature of this data obviously smoothes out many details of air-sea interaction). Our approach of completely ignoring the ice cover in the wave model means, however, that the established patterns of changes may be artificial in areas covered with ice during a large part of the year (such as the Bothnian Bay). The key distortion to instantaneous wave properties in ice-free regions of a partially ice-covered basin stems from the potential decrease in the fetch length for some regions and an associated overestimation of the wave heights and periods. Given the predominant wind direction from the SW in the northern Baltic Proper (Mietus, 1998) and the typical presence of sea ice in this area, it is very unlikely that the related distortions would qualitatively affect the established patterns in most of the Baltic Proper.
A key message from the described results is that many seemingly controversial trends and variations established in wave properties at different sites to a large extent reflect the natural spatial variability in the Baltic Sea wave fields. In this context, it is highly intriguing that in some areas the trends in the long-term average wave heights and in the highest wave properties are different.
Although it is obvious that the described changes are driven by wind fields, the background reasons and future extension of the resulting spatio-temporal variability in wave properties remain largely concealed. Clearly, a simple increase in the wind speed or a gradual turn in the predominant wind direction over the entire basin is not sufficient to produce such an extensive and strong pattern of variations in wave conditions. The reaction of the sea surface to changing wind conditions is generally a nonlinear process and the response in terms of the wave field not necessarily exactly follows the changes in the wind field similarly to the quite weak correlation between the temperatures of the air and surface water in the Black Sea (Shapiro et al., 2010).
A remarkable feature is the match between the areas that show high statistical significance of the modelled changes and the domains that exhibit substantial positive and negative changes in the wave heights. This feature suggests that different regions of the Baltic Sea basin have experienced widespread but essentially different changes in certain wind properties. For example, during the last 40 yr there has been a significant increase in the frequency of south-western winds and a decrease in southern and eastern winds all over Estonia (Kull, 2005). Such a change may be responsible for a large part of the increase in wave activity in the northern Baltic Proper as it leads to a systematic increase in the typical fetch length in this basin. This alteration, though, cannot explain the rapid variations in wave heights in the southern Baltic Sea.