# Long-Term and Decadal Sea-Level Trends of the Baltic Sea Using Along-Track Satellite Altimetry
## 4 Datasets
### Tide Gauge Data  
TG records provide an exclusive and comprehensive knowledge of sea-level changes and variations. However, they are land-bound, which means that the TG data reflect the RSL. Thus, to obtain the ASL, they need to correct for the VLM effect. In this study, the TG-derived ASL is compared with the SA-derived ASL trend estimates. The Baltic Sea has one of the world's densest observational tide gauge networks with remarkably long-term and high-quality local sea-level records [73]. Within the study area, 13 TG stations were selected that match the time span (1995-2022) of available SA data. Most TG stations provide hourly data for the entire study period, whereas a couple of used stations had only a few daily readings within the first decade of the study period. Some of the TG stations have longer data gaps due to the malfunctioning or change of the sensors; for more details, see Tables 2 and A1 and Figure 5b. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**ID**} & \multirow{2}{*}{**Station**} & \multirow{2}{*}{**Latitude [\({}^{\circ}\)]**} & \multirow{2}{*}{**Longitude [\({}^{\circ}\)]**} & \multirow{2}{*}{**Country**} & \multicolumn{2}{c}{**VLM**} & \multicolumn{1}{c}{**\(\Delta\)N**} & \multicolumn{1}{c}{**No. Hourly**} & \multicolumn{1}{c}{**Missing Hourly**} \\  & & & & & **[mm/yr]** & **[mm/yr]** & **Data (i)** & **Data [\%]** \\ \hline
1 & Dihami & 59.21 & 23.50 & Estonia & 3.09 & 0.4 & 117,833 & **51.99**1  & 0.4 & 244,427 & 0.42 \\
3 & Ventspils & 57.40 & 21.53 & Latvia & 1.56 & 0.3 & 200,199 & **18.41** \\
4 & Ustka & 54.59 & 16.85 & Poland & 0.13 & 0.1 & 175,622 & **28.45** \\
5 & Kolobrzeg & 54.19 & 15.55 & Poland & \(-\)0.06 & 0.1 & 170,399 & **30.58** \\
6 & Swinouscie & 53.91 & 14.25 & Poland & \(-\)0.18 & 0.1 & 175,157 & **28.64** \\
7 & Sassnitz & 54.51 & 13.64 & Germany & 0.09 & 0.1 & 237,694 & 2.58 \\
8 & Rodvig & 55.25 & 12.37 & Denmark & 0.62 & 0.2 & 226,479 & **7.73** \\
9 & Simrishamn & 55.56 & 14.36 & Sweden & 0.89 & 0.2 & 234,745 & 0.00 \\
10 & Kungsholmsfort & 56.11 & 15.59 & Sweden & 1.36 & 0.2 & 245,439 & 0.00 \\
11 & Marviken/Arkó 2 & 58.55 & 16.84 & Sweden & 3 & 4.46 & 0.4 & 245,448 & 0.00 \\
12 & Hanko & 59.82 & 22.98 & Finland & 4.16 & 0.4 & 245,448 & 0.00 \\
13 & Pori & 61.59 & 21.46 & Finland & 7.44 & 0.7 & 244,728 & 0.29 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Overview of the used TG data for the study period from 1 January 1995 to 31 December 2022. Significant (>18%) data gaps are highlighted in bold font. The selected TG stations are operated by the national tide gauge authorities. The TG readings refer to the corresponding national realization of the EVRS2000 (European Vertical Reference System 2000) vertical datum (e.g., [74]), the zero level of which is the Normaal Amsterdam's Peil (NAP). In addition, the TG zero level was transformed into the mean permanent tide system. The locations of TG stations are shown in Figure 5, where the VLM effect is illustrated in the background and the geoid rise (\(\Delta N\)) is also shown with red isolines; for more details, see Section 4.4. All the available TG hourly data were used for the ASL and RSL trend estimates as the ground truth. Note that the SA-derived \(DT_{SA\in\mathbb{GT}}\big{(}\varphi_{TG},\lambda_{TG},t_{cycle}\big{)}\) is also compared with \(DT_{TG\in SA\ cycle}\) in order to examine whether the SA data random and diverse temporal sampling is sufficient for deriving the SA-based ASL trend estimates. Therefore, to obtain \(DT_{TG\in SA\ cycle}\) using Equation (2), the \(DT_{TG}\) readings only within 2 h before and after the \(t_{cycle}\) time window (resulting in a total duration of 5 h for \(w\)) are included in the temporal interpolation (TG records beyond this specified time window are excluded). Consequently, if there is a gap in the TG record within the time window, \(w\), the resulting \(DT_{TG\in SA\ cycle}\) remain as a NaN value.