# Shipborne GNSS-Determined Sea Surface Heights Using Geoid Model and Realistic Dynamic Topography
## 4 Derivation of Offshore Dynamic Topography
### Estimation of Dynamic Bias Uncertainties at the Tide Gauge Locations  
Although DB changes temporally, over short timeframes (e.g., daily), the DB should remain relatively stable, as erratic behavior (such as sudden jumps, both spatially and temporally) would suggest a lack of consistency in the HDM-based DT. However, such a hypothesis first assumes a well-performing HDM (i.e., the HDM phases should match TG data). Figure 3 shows correlation coefficients between the NEMO-Nordic HDM and TG readings at the TG locations. It can be noticed that the (uncorrected) HDM-based DT is well correlated with the TG data, with coefficients being generally above 0.95. The only slight exception is TG\({}_{31}\) (refer to Figure 2), with a correlation coefficient of 0.87, likely due to its location in relatively confined waters. The NEMO-Nordic HDM phases, thus, appear to adequately match TG readings (also see [30]). High DB standard deviation of NEMO-Nordic HDM may, hence, reveal poorly-performing TGs. For instance, notice in Figure 4b the high DB variability at TG\({}_{9}\) and TG\({}_{41}\) (yellow dots; also refer to Figure 2) during the C1 campaign, whereas during the C2 (Figure 4d) and C6 (Figure 4f) campaigns, the DB remained relatively stable. Such behavior may be associated with stormy conditions during the second half of the C1 campaign, since the harbor of TG\({}_{9}\) is relatively vulnerable to extreme weather, and TG\({}_{41}\) is affected by westerly winds that rapidly accumulate water during storms. Described variations in a confined harbor may not represent the offshore conditions. Therefore, the first uncertainty component (\(\sigma_{1}\)) for DB was estimated as a moving standard deviation (centered at an observation epoch \(t^{H}\)) in the DB temporal domain:  
Figure 3: Correlation coefficients between TG and HDM data at the TG locations (based on all 792 h of used data, cf. Table 1). For better readability, only the top of the vertical scale is shown. \[\sigma_{1}\left(t^{H}\right)=\sqrt{\frac{1}{T-1}\sum_{m=t^{H}-\frac{T-1}{2}}^{t^{H} +\frac{T-1}{2}}\left[DB(\varphi^{TG},\lambda^{TG},m)-\frac{1}{T}\sum_{m=t^{H}- \frac{T-1}{2}}^{t^{H}+\frac{T-1}{2}}DB(\varphi^{TG},\lambda^{TG},m)\right]^{2}}, \tag{10}\]  
where \(T\) denotes the time extent considered at a certain time. A 25-h period was determined suitable, whereby a minimum of 12 h of data was included in all DB (and DT) computations, before and after the campaigns. This was done to avoid shorter than 25 h window sizes during the campaigns, which would have introduced inconsistency to the temporal domain uncertainty estimation. Since DB has a long-wavelength nature, the mean DB estimates at neighboring TG stations should ideally be similar in value. Therefore, discrepancies between mean DB estimates may reveal, for example, errors in TGs connections to height system(s) or near-shore processes. In the Gulf of Riga (cf. Figure 2), the mean DB estimates differ over relatively short spatial scales (Figure 4a,c,e); whereby, the discrepancies appear similar during all the campaigns. For instance, the mean DB at TG\({}_{17}\) always appears higher than at TG\({}_{16}\) and TG\({}_{18}\) (refer to Figure 2). A higher mean DB estimate can similarly be observed at TG\({}_{40}\). Such reoccurring discrepancies could indicate errors in the levelings that connect TGs to height system(s). Alternatively, the mean DB at TG\({}_{14}\) (refer to Figure 2) was significantly higher (more than usual) than at the neighboring TG stations during the C2 campaign (Figure 4c). According to the nearby weather station, during the second half of the C2 campaign, relatively strong winds (occasionally over 10 m/s) blew in the general direction of the exit of the harbor in which TG\({}_{14}\) resides. The receding water level in the harbor may, thus, have been a cause for a high mean DB estimate. Such behavior, however, does not represent offshore marine processes. Additionally [23], compared TG\({}_{4}\) readings to DT determined at the vessel's harbor, roughly 5 km away.