# Validation of Copernicus Sea Level Altimetry Products in the Baltic Sea and Estonian Lakes
## 2 Material and Methods
### In Situ Data  
The Estonian coastline has a dense tide gauge network, from which 23 (include two stations, Rannu-Joesuu (22) and Mustvee (23) in the lakes) stations were selected for the study (Figure 2). Of those, 15 stations are managed by the Estonian Environmental Agency (EEA) and 8 stations are operated by the Department of Marine Systems (MSI) of Tallinn University of Technology. All these tide gauges are equipped with pressure sensors and have operated for more than ten years [15]. In 2017-2018, the automatic tide gauges as well as tide gauge rods were reconnected to the national levelling network. The automatic tide gauges record hourly sea level anomaly (\(\mathit{SLA}_{\mathit{TG}}\)) in the Estonian height system (EH2000). The measurements are fully compatible with the European Vertical Reference System (EVRS), because the EH2000 essentially is a national realization of the EVRS in Estonia [24]. The tide gauge data were used to estimate sea-level deviations along each altimetry track. The tide gauge data were converted to the same reference system with satellite altimetry data by using geoid undulation (\(N\)) from the Estonian geoid model EST-GEOID2017 (Equation (4)). Since the geoid model has been fitted to vertical datum, geoid surface at the tide gauge approximately coincidences with the vertical datum zero. Therefore, instantaneous \(\mathit{SLA}_{\mathit{TG}}\) relative to geoid was calculated from the four tide gauge records nearest to the satellite track at the time of the satellite overpass. \(\mathit{SSH}_{\mathit{TG}}\) above the ellipsoid WGS84 at each Sentinel-3 footprint can thus be presented as:  
\[\mathit{SSH}_{\mathit{TG}}=\mathit{SLA}_{\mathit{TG}}+N. \tag{4}\]  
For Sentinel-3 validation, the difference between \(\mathit{SSH}_{\mathit{SA}}\) and \(\mathit{SSH}_{\mathit{TG}}\) was calculated using the following equation:  
\[\Delta\mathit{SSH}_{\mathit{TG}}=\mathit{SSH}_{\mathit{SA}}-\mathit{SSH}_{ \mathit{TG}}. \tag{5}\]  
Residual difference \(\Delta\mathit{SSH}_{\mathit{TG}}\) was further analysed. The \(\Delta\mathit{SSH}_{\mathit{TG}}\) residuals larger than 2.5 STD were considered outliers. Residuals were plotted against distance from the coast (Figure 4). Correlation plots between \(\mathit{SSH}_{\mathit{SA}}\) and \(\mathit{SSH}_{\mathit{TG}}\) were compiled as well. In addition, GNSS kinematic measurements on the vessels were used to validate \(\mathit{SSH}_{\mathit{SA}}\) over the study sites. Multiple-frequency Trimble R8s and Trimble R4-3 receivers were mounted on top of the vessel (Figure 5b). Antenna reference points were connected to the sea level (\(H\) in Figure 3) using a total station (Figure 5a). Two antennas were used to eliminate the risks when one receiver stops working and to filter out vessel fluctuations [25; 26]. Measurements were carried out on the same day of the satellite overpass; the weather was calm during all measurements (Table 2). GNSS measurements were recorded at 2 s intervals along the altimetry ground tracks (Figure 2). The first data quality control was performed on board the vessel with the program TEQC [27]. The GNSS base stations  
Figure 4: An example of the effect of the coastal zone on Sentinel-3 data. S3A pass 186 cycles 40–51 sea surface height (\(\mathit{SSH}_{\mathit{SA}}\)) was compared with the geoid-based sea surface height (\(\mathit{SSH}_{\mathit{TG}}\)), Equation (5), in the Gulf of Riga. The grey and red lines indicate the coast and the distance (2 km) from the coast, respectively. data from the Estonian Permanent GNSS Network ESTPOS [28] and the Trimble Business Centre software were used for kinematic data processing in double difference mode. The International GNSS Service (IGS) precise ephemeris and absolute antenna calibration data were used. First, both receiver's data were processed separately and \(SSH_{GNSS}\) above the ellipsoid from two receivers were compared.