# Validation of Copernicus Sea Level Altimetry Products in the Baltic Sea and Estonian Lakes
## 2 Material and Methods
### Sentinel-3 Data Products  
Sentinel-3 satellites carry a dual-frequency SAR altimetry payload. The main frequency used for range measurements is the Ku-band (13.575 GHz), while the C-band (5.41 GHz) is used for ionospheric correction. The SRAL altimeter has high resolution in the along-track (300 m) and across-track (1.64 km) directions, which gives better results in the coastal areas [20] compared with the conventional pulse-limited radar altimeter. Sentinel-3 is operating in a sun-synchronous orbit with a repeat cycle of 27 days. Combining S3A and S3B, the repeat cycle between two satellites becomes 13.5 days on a regional scale and the interval between interleaved groundtracks is 27 km near the Equator, which offers a better temporal and spatial resolution and increases the chance of passing over small waterbodies. For this study, Sentinel-3 SRAL Non Time Critical Level-2 product (SR_2_LAN) from the Estonian National Copernicus Hub (ESTHub) mirror site ([[https://ehdatahub.maaamet.ee/dhus/#home](https://ehdatahub.maaamet.ee/dhus/#home)]([https://ehdatahub.maaamet.ee/dhus/#home](https://ehdatahub.maaamet.ee/dhus/#home))) over the period from December 2018 to November 2019 were used. Note that the radar range measured between the satellite and the sea surface observed near the nadir is affected by several error sources when the signal passes through the atmosphere. Additionally, several tidal effects are involved in measuring the sea level. The corrections were provided by the data agency. The following atmospheric and geophysical corrections were used:  
\[\sum\!\!pole tide height); \(h_{a}\) is inverted barometer height correction, and \(h_{f}\) is high frequency fluctuations of the sea surface topography correction. All these parameters are given along with each SR_2_LAN data file. More details can be found in ESA's technical guides for Sentinel-3 SRAL/MWR Level 1 & 2 [21].  
Following that, the corrected range between the satellite and the sea level was calculated:  
\[R_{cor}=R+\sum\limits_{i}{cor}, \tag{2}\]  
where \(R\) is the directly measured distance or pseudorange between the satellite and the sea level (Figure 3). The distance is estimated with the off-centre-of-gravity (OCOG) retracking algorithm [22; 23]. \(SSH_{SA}\) above the ellipsoid was calculated:  
\[SSH_{SA}=h_{SA}-R_{cor}, \tag{3}\]  
where \(h_{SA}\) is satellite height above WGS84 ellipsoid, which can be calculated using satellite ephemeris. \(SSH_{SA}\) values were calculated for all studied S3A and S3B ground tracks (Figure 2) over the period from 1 January 2019 to 1 November 2019, equivalent to 10-11 cycles for each pass. The SAR mode of Sentinel-3 effectively reduces land-induced contamination in the radar signal by increasing the spatial resolution along the track. However, the problem still exists when the satellite azimuth direction and the coastline are not perpendicular. Therefore, Sentinel-3 measurements within 2 km of the shoreline were removed in order to reduce the influence of potentially noisy data, as demonstrated by the blue points appearing between the grey and red lines in Figure 4. Normally, the differences (\(\Delta SSH_{TG}\)) between \(SSH_{TG}\) and \(SSH_{SA}\) remained within 0.5-1 m. However, some \(\Delta SSH\) outliers could be up to 2 m or more on open water due to reflections from small islets or vessels, which is known as the 'hooking effect' in off-nadir measurements. In addition, coastal TG data can be influenced by coastal effects (such as storm surges, wave setup), while these effects are relatively small off the shoreline. Figure 3: Schematic plot of the relationship between the sea surface height measured by satellite altimetry (\(SA\)), tide gauge (\(TG\)) and GNSS on the vessel (\(GNSS\)). Abbreviations meaning: \(SSH\)—instantaneous sea surface height, \(SLA\)—instantaneous sea-level anomaly, \(h\)—ellipsoidal height, \(N\)—geoid undulation, \(R\)—distance between the satellite and the sea surface, \(H\)—GNSS antenna height from the sea surface.