# Long-Term and Decadal Sea-Level Trends of the Baltic Sea Using Along-Track Satellite Altimetry
## 5 Results
### Long-Term ASL Trend  
The long-term (1995 to 2022) ASL trend results using both SA and TG are illustrated in Figure 7. The ASL trends are calculated using (i) hourly TG observations (dark blue); (ii) TG-derived \(DT_{TG@SA~cycle}\) (light blue); and (iii) SA instantaneous data (red). The RMSE of the paired estimates for all stations are computed by Equation (10), where \(\beta^{o}\) is either \(trend(DT_{TG})\) (Figure 7b) or \(trend(DT_{TG@SA~cycle})\) (Figure 7c), whereas \(\beta^{e}=trend(DT_{SA})\). The comparison of the TG and SA sea-level trends also reveals a spatial variability among the stations (Figures 7 and 8). In the north-eastern study area, certain stations (such as Pori, Hanko, Ristna, and Marviken) exhibit higher sea-level trend values (observed in both SA and TG) ranging around \(4\) to \(5\) mm/yr. Previous studies have also noted larger  
Figure 7: SA- and TG-derived ASL trend estimates for the period 1995 to 2022. (**a**) Spatial distribution of the SA (red)- and hourly TG (blue)-based trend estimates. (**b**) Estimated trends using both instantaneous SA (red) and TG hourly data at each station (dark blue) with the corresponding RMSE = \(1.5\) mm/yr, and (**c**) \(DT_{TG@SA~cycle}\)-based trend (light blue) compared with instantaneous SA-derived trend (red), with the corresponding RMSE = \(1.2\) mm/yr. The whiskers in (**b,c**) represent the estimated trend uncertainties within the 95% confidence error of each dataset. The green line in (**a**) divides the study area into north-eastern and south-western sections. ASL trends in the north-eastern Baltic Sea region (e.g., [29; 45; 46; 63]). This was suggested to be attributed to fluctuations in air pressure [79; 80] and intensified westerly winds that push the water masses toward the north-east [29; 63]. Additionally, a poleward shift in low-air-pressure systems was observed, contributing to local sea-level increases via the inverted barometer effect. Moreover, an increased influx of freshwater from the northern Baltic Sea has been suggested as a factor leading to the rise in the mean sea level over the northern and western Baltic Sea sections [63]. However, within the south-western section, the trend values mostly varied between 2 and 4 mm/yr. Notably, stations Rodvig (#8) and Kungsholmsfort (#10) revealed large TG-derived trend values of nearly 5 mm/yr (Figure 7). At most stations, the sea-level trends of \(DT_{SA@TG}\) and \(DT_{TG}\) data (Figure 7b) vary from 2.1 to 5.4 mm/yr. A closer examination of individual stations in Figure 7b reveals that 9 stations (out of 13) agreed within \(\pm\)1 mm/yr. The most notable differences appear to occur at stations Ventspils (#3, with a difference of 3.3 mm/yr), Ustka (#4, difference of 1.7 mm/yr), Rodvig (#8, with a difference of 2.6 mm/yr), and Hanko (#12, with a difference of 1.9 mm/yr) (cf. Figure 7b). Similarly, the \(DT_{SA@TG}\) and \(DT_{TG@SA\ cycle}\) trends (Figure 7c) vary overall from 1.3 to 5.8 mm/yr. The differences in the \(DT_{SA@TG}\) and \(DT_{TG@SA\ cycle}\) trends in Figure 7c indicate that out of the 13 stations assessed, only the trends of six stations remain within a \(\pm\)1 mm/yr tolerance. Broadening the allowable differences to \(\pm\)1.5 mm/yr, however, revealed that 11 out of 13 stations are in agreement. The largest differences were determined at the TG stations Rodvig (#8) and Kolobrzeg (#5), with 2.5 mm/yr and 1.5 mm/yr, respectively. Further examination suggests that large differences within the range of 1-1.5 mm/yr may indicate issues with the SA or TG data for these specific stations. For instance, trend estimates are potentially affected by extensive data gaps (cf. Table 2, Figure 8) in stations such as Dirhami (#1), Ventspils (#3), Ustka (#4), Kolobrzeg (#5), and Swinoujscie (#6). Moreover, upon examining individual stations, it became evident that the \(DT_{SA@TG}\) and \(DT_{TG}\) pairs tended to yield more reliable results, showing agreement within a difference of \(\pm\)1 mm/yr.