# Shipborne GNSS-Determined Sea Surface Heights Using Geoid Model and Realistic Dynamic Topography
## 6 Discussion
### Dynamic Bias Prediction Method  
Previously, refs. [15; 30] used exact interpolators to predict offshore DB (required for correcting the used HDM for DT determination). Such an approach inherently assumes that there are no errors in the TG data and TGs connections to the height system(s), as well as that the estimated DB at a TG station is an expected value for all nearby offshore locations. In Section 4.1, it was suggested that this might not be the case. Therefore, a new approach was developed for estimating DB uncertainties and predicting offshore DB with an inexact interpolator (least-squares collocation) employing these estimates. The difference between an exact and inexact interpolator is now investigated.  
A well-performing inverse distance weighted interpolation method (out of various exact interpolators, this one appears to provide the best results--[PERSON], personal communication, September 2021) was used to predict offshore DB. A comparison with the developed approach is presented in Figure 18a. Notice that the residuals of the inverse distance weighted method are more spread out and biased; thus, highlighting the significant impact of the DB prediction approach on the results. Since the developed approach does not require the predicted DB to follow estimates at the locations of TG stations, the differences between the two histograms are primarily the direct impact of potentially erroneous (or misleading, since DT at TG stations may not represent offshore conditions) TG data.  
Figure 18b presents residuals of the C2 campaign, derived using inverse distance weighted interpolation to predict offshore DB. Notice the residuals over a decimeter near TG\({}_{14}\), whereas no such residuals appeared when the newly developed method was used (cf. Figure 17). This difference is a direct cause of the issue described in Section 4.1, where the estimated DB at TG\({}_{14}\) was significantly higher (more than usual) than at the neighboring TG stations, likely due to offshore-directed strong winds, which may have pushed the water away from the harbor (i.e., lower TG readings result in higher DB, cf. Equation (3)).  
An alternative example from Section 4.1 can also be further discussed. Namely, a significant contributor to the more negative bias of the inverse distance weighted method in Figure 18a is TG\({}_{4}\). It was demonstrated in [23], how the DT at TG\({}_{4}\) was up to 8-9 cm higher in comparison to the vessel's nearby harbor (higher DT results in lower residual values, cf. Equation (2)). Relatedly, differences around a decimeter appeared for campaigns C2 and C3 near TG\({}_{4}\), between the inverse distance weighted method and the developed approach. These examples show how near-TG localized phenomena propagate to the estimated offshore DB with exact interpolators and demonstrate the superior performance of the developed approach.  
Figure 18: (**a**) Histograms of residuals (all campaigns combined): the impact of the DB prediction method, and (**b**) filtered, corrected, and least-squares adjusted residuals, derived using inverse distance weighted interpolation for DB prediction. Numbered circles in (**b**) denote the used TG stations.