# Long-Term and Decadal Sea-Level Trends of the Baltic Sea Using Along-Track Satellite Altimetry
## 4 Datasets
### Vertical Land Motion and Geoid Rise Models  
In order to obtain the ASL trend values from the TG-derived RSL, the VLM needs to be considered. VLM may occur due to glacial isostatic adjustment (GIA), tectonic motion, and anthropogenic effects. Over the Baltic Sea region, VLM is dominated by GIA, caused by ice shield melting after the last deglaciation over the Fennoscandia. Slow crustal recovery from the pressure of the ice sheet that covered the area during the last glacial period causes post-glacial land uplift up to around 10 mm/yr in the north part of the sea (centre of the former ice sheet) and decreases to nearly zero at the edges of the former ice sheet (south). The southern part of the Baltic Sea therefore experiences a land subsidence as a compensating effect. This causes the RSL to increase in the north and decrease in the south part of the Baltic Sea, as can be seen from TG records (cf. Figures 5 and 6). In recent decades, an acceleration has been seen in the long-term sea-level trends since the 1960s [77], consistent with the global signal [2]. On the other hand, SA and GPS (Global Positioning System) provide independent measurements of sea-level change and VLM, with respect to a global geocentric coordinate system. To assess the separate effects of sea-level change and land uplift, accurate information on land uplift is essential in the Baltic Sea region, as the VLM value varies throughout the region. In this study, the land uplift effect is removed from TG observations using the NKG2016 LU model to convert the TG readings (\(DT_{\textit{obs}}\)) to the actual DT (\(DT_{\textit{TG}}\)), i.e., relative to the Earth's centre of mass. This model includes the latest GIA land uplift model for the Baltic Sea region, developed by the Nordic Commission of Geodesy (NKG, www.nordicegeodeticcommission.com (accessed on 26 August 2021), and it covers an area from 49\({}^{\circ}\) to 75\({}^{\circ}\)N and 0\({}^{\circ}\) to 50\({}^{\circ}\)E [75]. The VLM correction reference time epoch (i.e., \(t_{0}=2000.0\)) is applied to the TG observation time record (i.e., \(t_{i}\)) by adding it to the TG readings using Equation (1). Also, the geoid change (\(\Delta N\)) is primarily due to GIA, which causes a rise in the geoid in the Baltic Sea (cf. Figure 4). The \(\Delta N\) rate is approximately 10-15% of the VLM rate in the Baltic Sea [34]. Figure 6 shows annual DT variations of TG observations (hourly data) before (black) and after (blue) VLM correction for six selected TG stations.  
In this study, both RSL and ASL are considered for trend estimation, as illustrated in Figure 6 (RSL in black and ASL in blue dots) to illustrate the VLM effect. This figure shows the annual DT variation of six selected TGs (one for each country), for example, before (black) and after GIA correction (blue). Accordingly, a significant deviation of ASL and RSL can be observed over intense land uplift areas (e.g., the Pori and Hanko stations), as was expected. The dots show the average DT of each year, and the bars represent the maximum and minimum DTs, whereas the STD of the annual MDT value varies within 5 to 8 cm. Additionally, the annual fluctuation in MDT, calculated as the difference between the maximum and minimum MDT values for each year, ranges from 20 to 30 cm during the period from 1995 to 2022 across all stations. These significant fluctuations in annual MDT could result in a notably high degree of variability in estimated sea-level trends, particularly when using short-term time-series data. Also, Figure 10 represents the median values and the 25 th and 75 th percentiles of the annual DT variations for six stations (the same as in Figure 6).