# Shipborne GNSS-Determined Sea Surface Heights Using Geoid Model and Realistic Dynamic Topography
## 3 Shipborne GNSS Surveys, Data, and Other Used Information
### Hydrodynamic Model and Tide Gauge Data  
Previous works [11; 15; 30; 43] have evaluated the ability of the various HDMs available for the Baltic Sea in deriving sea surface dynamics. Based on these assessments, all the models contain a DB relative to the used height reference (i.e., BSCD2000), whereby the bias varies between models. It also appears that, generally, the most accurate representation of sea surface dynamics in the region can be obtained from the high-resolution (hourly data, with a spatial resolution of approximately 1.0 nautical miles) NEMO-Nordic model [44; 45], which was, thus, also chosen for DT determination in this study. If TGs are connected (e.g., by geodetic leveling) to the used height system(s), the DB in the NEMO-Nordic-based DT can be estimated using TG readings. This study employed hourly data from 41 TG stations: 15 Estonian, 7 Latvian [46], 11 Swedish [47], 7 Finnish [48], and one Russian [49] (cf. Figure 2). Note that the NEMO-Nordic model and Russian TG data should be first converted from mean-tide to the zero-tide permanent tide concept for compatibility with the Estonian, Latvian, Swedish, and Finnish TG data [26] (and the normal heights discussed at the end of the previous section). Moreover, the Latvian [50] and Finnish [26; 51] TG readings are initially given relative to alternative height reference levels. Hence, before utilization, these data must be converted relative to the used height reference (i.e., national height systems compatible with the BSCD2000).  
Even though the Estonian, Latvian, Swedish, and Finnish height systems are all EVRS-based and heights refer to the Normaal Amsterdam Peil (NAP), some minor discrepancies exist (an additional discussion can be found in [26]). Thus, the pan-continental EVRF2019 [52] solution-based height system discrepancies can improve TG data compatibility further. Since GNSS post-processing was conducted relative to the Estonian and Latvian GNSS-CORS, the respective height systems were considered the zero level. The EVRF2019 solution yielded a \(-1\) cm correction to the Swedish and Finnish TG readings. On the other hand, the Russian TG data are given relative to the Baltic Height System of 1977 (BHS77), and a +21 cm offset had to be added.  
Similarly to the geodetic networks, the Baltic Sea TG networks are also deforming due to VLM. Even though the zeros of TGs approximately coincide with the reference level at the (common) reference epoch of the national height systems, in the land uplift regions, the zero separates from the reference, yielding lower than actual sea level readings (i.e., DT relative to the nearby solid Earth; cf. Figure 1). The principles outlined in [26] were, hence, employed to obtain absolute DT (i.e., relative to the height reference):  
\[DT_{TG}\Big{(}\varphi^{TG},\lambda^{TG},t^{H}\Big{)}=DT_{RSL}\Big{(}\varphi^{ TG},\lambda^{TG},t^{H},t_{0}\Big{)}+VLM_{leveled}\Big{(}\varphi^{TG},\lambda^{TG} \Big{)}\cdot\Big{(}t^{H}-t_{0}\Big{)}, \tag{9}\]  
where \(DT_{TG}\) and \(DT_{RSL}\) are the TG-based absolute and relative DT at an observation epoch \(t^{H}\) (hourly temporal resolution), respectively, and \(VLM_{leveled}\) denotes leveled VLM rate at a TG station (obtained from the NKG2016 LU VLM model). The term \(t_{0}\) denotes the reference epoch of a height system to which the derived \(DT_{TG}\) refers. These TG data, corrected for datum offsets and VLM, were then used for linking the NEMO-Nordic HDM to the used height references for offshore DT derivation.