Changes in the Water Surface Level of the Baltic Sea from Satellite Altimetry and Gravity Missions

Figure 1 and 2 compare the altimetric (SSHA) and gravimetric (EWT JPL) anomalies of the Baltic Sea level between 2001 and 2021, both before and after the removal of seasonal signals. The altimetric anomalies are consistently about 10 cm higher than the gravimetric anomalies, regardless of the presence of seasonal signals, which is because satellite altimetry considers factors such as temperature, salinity, tides, and ocean currents, while gravimetry includes mainly the changes in Earth's mass distribution. Furthermore, it should be noted that the GRACE mission may underestimate the impact of glacier melting on sea level rise by about 30% due to the limited spatial resolution of the data. Conversely, the growth of the EWT indicator may be caused by the uplift of land masses due to post-glacial rebound, which is discernible in Scandinavia (Wahr and Velicogna, 2003; Chambers et al., 2007; Milne et al., 2009; Steffen, Müller and Denker, 2009). However, it is important to note that the impact of post-glacial rebound is majorly considered from GRACE solutions due to GIA correction. Consequently, this factor has a rather limited influence on our results.

Figure 1.

Figure 2.

Discontinuity of data is evident in the gravimetric time series. The first gap is a result of the start of the Gravity Recovery and Climate Experiment (GRACE) mission on 03.17.2002, while the second gap occurred between the end of the GRACE mission and the start of the GRACE-Follow On (GRACE-FO) mission. The lack of gravimetric data at the beginning of the period may increase the trend line slope coefficient, which should be taken into account during the interpretation of results.

We can observe that the impact of seasonal signals on altimetric and gravimetric anomalies is minor. Removing the seasonal signal slightly decreases the annual sea level rise trend for both SSHA from 0.62 to 0.58 cm/yr and for EWT JPL from 0.95 to 0.91 cm/yr. The difference between these results oscillates close to the measurement uncertainty value of ±0.04 cm/yr (Chen, Wilson and Tapley, 2013; Watson et al., 2015).

Figure 3 and 4 reveal a strong positive linear relationship between altimetric anomaly values and the EWT index from the JPL center. The linear regression coefficients are 0.72 before the removal of the seasonal signals and 0.71 after the removal of seasonal signals, indicating moderate-to-strong positive linear relationships. Consequently, we can interpret that a 1.00 cm increase in the altimetric anomaly value corresponds to a 0.71–0.72 cm increase in the EWT index. Lower values for gravimetric anomalies may result from not taking into account factors such as sea surface temperature or salinity, which impact the water density, and underestimating the impact of glacier melting by the GRACE mission.

Figure 3.

Figure 4.

The coefficient of determination R² is 0.84 and the coefficient of Pearson linear correlation R is 0.92 in Figure 3 and 4, indicating a strong positive linear relationship between these variables. However, the time series from CSR shows a poorer agreement with the satellite altimetry results than JPL, which will be examined in more detail when discussing Table 2.

Figure 5 and 6 depict a comparison between altimetric anomalies (SSHA) and sea surface temperature (HRSST) from 1993 to 2018, both before and after eliminating seasonal signals. We can see significant changes in the HRSST range after removing seasonal signals (from 0–19°C to –2–2°C). The remaining temperature anomalies after removing the seasonal effects are caused by the variability of the seasons including El Niño events. Local maxima and minima in the deseasoned time series of sea surface temperature may be caused by short-term weather fluctuations, climate variation, different hydrologic conditions, and changes in the marine ecosystem of the Baltic Sea.

Figure 5.

Figure 6.

In contrast, the trend line slope coefficient of sea surface temperature is the same both before and after removal of the seasonal signals and amounts to 0.04°C/yr. We can conclude that, although the seasonal signal affects the range and character of the oscillations, the increase in value over time itself follows a very similar pattern.

While analyzing the altimetric anomalies for 1993–2018, we can notice very comparable results and dependencies as for 2001–2021. However, the secular trend is lower by about 0.07 cm/yr than the same trend from 2001–2021, which can be the result of the presence of observations from the 1990s, when the rate of mean sea level rise was lower.

Figure 7 and 8 show the major impact of removing the seasonal signal on the linear regression parameters between altimetric anomalies and sea surface temperature. After the removal, the linear regression coefficient increases from 0.26 to 3.55 cm/°C, indicating that a change of sea surface temperature by 1°C corresponds to a change of sea level height by 3.55 cm. We can observe a similar growth for the coefficient of determination R² and the Pearson correlation coefficient R, which increased from 0.01 to 0.07 and from 0.11 to 0.26 before and after the removal of the seasonal signals for R² and R, respectively. Nevertheless, this is still a rather weak positive correlation between these variables.

Figure 7.

Figure 8.

We can obtain the projected sea level rise due to the change in sea surface temperature by multiplying the annual sea surface temperature rise trend by the linear regression coefficient. For the deseasoned data, the temperature component is equal to 0.13 cm/yr. Considering that the sea level rise trend from altimetric measurements for the same period was 0.51 cm/yr, we can conclude that sea surface temperature rise was responsible for about 25% of the sea level rise in the Baltic Sea. Chen et al. (2013) presented similar results for the global sea level rise trend, where the steric part was 0.06 cm/yr, which was 25% of the total value (0.24 cm/yr). An even closer outcome can be found on the website of NASA (https://sealevel.nasa.gov), where the increase in the steric height of the sea is 0.13 cm/yr at the time of access on February 16, 2024. Nonetheless, we should note that the cited results also considered the salinity factor, while we study only sea surface temperature impact in our research.

Table 2 and Tables A1–A3 from the Appendix A show the results of the comparison for different gulfs and parts of the Baltic Sea including altimetric (SSHA), gravimetric (EWT), and sea surface temperature (HRSST) data. We visualize them in the following bar charts and choropleth maps to show relevant trends, dependencies, and patterns in Baltic sea level changes. They depict the variability of individual values across the Baltic regions during specific periods. The analysis considers the area of the Baltic Sea (the whole area), the Gulf of Gdańsk, the Gulf of Bothnia, the Gulf of Finland, and the Gulf of Riga, as well as the central part of the Baltic Sea.

From the results presented in Table 2, Tables A1–A3, and Figure 9–Figure 10, a relatively large variability emerges of sea level rise linear trends derived from the altimetric data. This large variability is clearly visible between the following 5-year periods and between different parts of the Baltic Sea. The largest positive secular changes in sea surface level come from 2016–2021 and they exceed 1 cm/yr in almost all studied areas except for the Gulf of Gdańsk, whose sea level rise trend is 0.8 cm/yr. The period 2006–2011 is considerably distinguishable because we can perceive at that time a negative sea level rise trend in all areas, which oscillates around the value of −1.8 cm/yr. The observed anomaly could probably be caused by high air temperatures and repeated heat waves during this period. For example, the 2006 heatwave that affected a large part of Europe resulted in increased water evaporation and drying up of riverbeds that are tributaries of the Baltic Sea (Rebetez, Dupont and Giroud, 2009; Chiriaco et al., 2014). A reflection of this phenomenon can also be found in Figure 20 with a clear pattern of increased sea surface temperatures in all areas of the Baltic Sea in 2003–2008.

Figure 9.

Figure 10.

When comparing the results of the 5-year time series from 2001–2021, we can notice that short 5-year periods are characterized by irregular and divergent values. This may be due to the great sensitivity of these data to seasonal effects and short-term factors, such as rapid changes in weather and climate, wave heights, or freshwater inflows into the sea.

Conversely, the values of the sea level rise trend from the entire 2001–2021 period present a great consistency between various parts of the Baltic Sea. The results range from 0.55 to 0.62 cm/yr, with the slowest sea level rise trend observed in the central part of the Baltic Sea and the fastest in the Gulf of Finland, where post-glacial rebound effects additionally occur. Obtained values from this study are greater than the results of Łyszkowicz and Bernatowicz (2019) for the southern coast of the Baltic, which oscillated between 0.26 and 0.36 cm/yr (Łyszkowicz and Bernatowicz, 2019). They also surpass the global sea level rise trend ranging between 0.24 and 0.36 cm/yr (Milne et al., 2009; Chen, Wilson and Tapley, 2013; Watson et al., 2015), but considered different time spans.

Figures 11 and 12 compare the sea level rise trends derived from altimetric (SSHA) and gravimetric data – EWT from JPL and CSR centers. Figure 11 shows substantial linear trends for EWT in the period 2001–2006. The values exceed SSHA results by 2.45 cm/yr for JPL and by 2.00 cm/yr for CSR, for the entire area of the Baltic Sea. However, a distinct outlier in gravimetric anomaly observation from JPL can be observed in the central part of the Baltic Sea in the same period. There, the trend reaches the value of 39.06 cm/yr. Such high values of linear trends for EWT data in 2001–2006 are due to measurement discontinuities in GRACE missions, which lasted until March 2002, and due to poor data quality in the first months of the mission. In subsequent 5-year periods, the values of the annual sea level rise trends for the gravimetric data are already comparable or lower than the trend values from the altimetric data. In general, we can observe that for most of the analyses, the absolute values of linear trends are higher for the JPL center than for the CSR center. This may be caused by different processing strategies and the background models, as well as differences in outlier elimination methods and corrections for the Earth's oblateness value between these two analysis centers.

Figure 11.

Figure 12.

Figure 12 shows the sea level rise trends for the Gulf of Bothnia, the Gulf of Finland, and the Gulf of Riga, considering the presence of the seasonal signal in 2001–2021. The seasonal signal has a negligible effect on considered time series with the exception of EWT data from CSR in the Gulf of Finland and the Gulf of Riga. In the Gulf of Riga, after removing the seasonal signal from EWT data from CSR, the linear trend reversed, changing from −0.03 to 0.28 cm/yr. The large gravity anomaly values from the JPL center are evident once again. In comparison to the Gulf of Finland and the Gulf of Bothnia, the value of EWT JPL for the Gulf of Gdańsk is lower by about 0.5 cm/yr. This difference is likely caused by the land uplift of Scandinavia and Finland due to post-glacial rebound. We can also notice this dependency in Figure 13.

Figure 13.

Figure 14 and 15 show linear regression coefficients between altimetric anomalies and gravimetric anomalies. When analyzing results from Figure 14, we can state that the largest linear dependency occurs in the Gulf of Finland, the central part of the Baltic Sea, and the whole Baltic Sea area. The Gulf of Riga and the Gulf of Gdańsk are characterized by the weakest linear dependency, which can be related to the size of these gulfs, which can hardly be separated in GRACE data. We can observe similar patterns in all studied periods from Figure 14. The highest linear regression coefficients appear in 2001–2006; for the Gulf of Finland, the regression coefficients reach even 0.9. The second highest values of linear correlations come from 2001–2021. We can assume that this is due to the long-term nature of the observations, which makes the correlation between the analyzed data more visible. Further observation is a slight variation between different periods in Figure 14, which can be the result of weaker sensitivity of linear dependency between SSHA and EWT to short-term seasonal signals.

Figure 14.

Figure 15.

By examining Figure 16, we can assess the effect of the choice of gravimetric data processing center and the removal of the seasonal signal on the strength of the linear correlations. The analysis reveals a stronger linear relationship between the SSHA-EWT JPL data and the SSHA-EWT CSR data. For instance, in the Baltic Sea between 2001 and 2021, the linear regression coefficient for the SSHA-EWT JPL data is 0.71, while for the SSHA-EWT CSR data set it is only 0.51. This dependency is consistent across all periods and areas analyzed in the figure.

Figure 16.

The influence of the removal of the seasonal signal on the value of the linear regression coefficient is more apparent in the SSHA-EWT CSR dataset. Excluding the 2001–2006 period, the removal of the seasonal signal generally slightly weakens the linear correlation between the data. This is particularly noticeable for the 2011–2016 period, where the difference between the linear regression coefficients is typically around 0.1.

Figure 17–19 show the distribution of Pearson correlation coefficients between different sets of altimetric and gravimetric data. Similar to the linear regression coefficient, the EWT JPL data exhibits a stronger correlation with the SSHA compared to the EWT CSR. However, the differences are not as significant as in Figure. An exception to this is the Gulf of Gdańsk from 2001–2021, where the correlation after removal of the seasonal signal between the SSHA-EWT JPL data is 0.88, while the SSHA-EWT CSR correlation is only 0.68.

Figure 17.

Figure 18.

We can see both in Figure 15 and Figure 19 that the Gulf of Gdańsk and the Gulf of Riga are distinguished by a weaker linear dependency between altimetric and gravimetric anomalies. This may be due to the greater vulnerability of these bays to the effect of sea temperature on the increase in sea surface elevation, which is not included in gravimetric measurements, as well as the small areas of these gulfs. We can confirm this assumption in Figure 23 and Figure 24, where the Gulf of Gdańsk and the Gulf of Riga stand out with the highest Pearson correlation coefficients between sea surface temperature and altimetric anomalies in 1993–2018.

Figure 19.

Figure 20–24 show the results of analyses of sea surface temperature rise and its impact on altimetry anomalies measured in 1993–2018. In Figure 20, we can perceive the high sensitivity of the 5-year time series of sea surface temperature to the removal of seasonal signals, resulting in a significant decrease in the values of the linear trend. This is apparent in 2003–2008, where, as a result of removal of the seasonal signal, the linear trend falls from 0.55°C/yr to 0.11°C/yr. The linear trend results for the long-term time series (1993–2018) are characterized by substantial high resistance to the impact of removing the seasonal signal. In most of the considered Baltic Sea regions, these results remain essentially unchanged. Nonetheless, the Gulf of Gdańsk shows a deviation from this pattern, as the linear trend after the removal of the seasonal signal decreased from 0.07°C/year to 0.04°C/year during the period 1993–2018.

Figure 20.

Figure 21.

The highest values of sea surface temperature linear trend occur in 2003–2008. It can be associated with factors such as weather variabilities and climate changes, the inflow of hot tropical air, the inflow of warm waters from the North Sea, or human activities (Dutheil et al., 2022). The heat waves that affected Europe in 2006 are worth mentioning again (Rebetez, Dupont and Giroud, 2009; Chiriaco et al., 2014). While analyzing the 1993–2018 period, we can conclude that the largest trend of sea surface temperature rise takes place in the Gulf of Finland and the Gulf of Riga and it reaches 0.07°C/yr. This may be due to the shallowness of the mentioned gulfs. The average depth of the Gulf of Finland is 38 m, while that of the Gulf of Riga is 26 m. In the shallow gulf, the warming of seawater may occur faster and more intensely.

Figure 22 illustrates linear regression coefficients between altimetric anomalies (SSHA) and sea surface temperatures (HRSST). Because of the distinct advantage and much smaller variations of deseasoned data over seasoned data, sometimes as much as seven times, we can conclude that altimetry anomalies are sensitive to sea surface temperature changes caused by unseasonal, long-term factors such as global warming. Furthermore, while analyzing the results after removing the seasonal signals, we can see a rather irregular distribution of values over consecutive years. This is particularly noticeable in the Baltic Sea and the Gulf of Finland, where the differences are approximately 2.5–3.0 for consecutive periods. Meanwhile, the highest linear regression coefficient is found in the Gulf of Gdańsk for the long-term period of 1993–2018, with a value of 3.69.

Figure 22.

In Figure 23, which depicts the values of Pearson correlation coefficients, we can observe a similar trend, where the values of deseasoned data are larger than those including seasonal signals. However, these differences are not so large as in Figure 22. The largest values occur in the Gulf of Riga and the Gulf of Finland, where they can reach up to 0.2. We can also notice that in all areas of the Baltic Sea, the largest correlation coefficients come from the periods of 2003–2008 and 2008–2013. In the long-term 1993–2018 period, the highest correlation between altimetry anomalies and sea surface temperature is found in the Gulf of Gdańsk (0.31), the Gulf of Riga (0.30), and the Gulf of Finland (0.29). Considering the nature of the data, we can assess these results as a positive and moderately strong correlation. In Figure 24, we can see that the Gulf of Bothnia has the smallest linear regression and Pearson correlation coefficients.

Figure 23.

Figure 24.