## 3 Research and Results
### Composite Estimation Comparison  
We observed that all three models performed inconsistently over Sentinel-2 images from different dates, which motivated the use of a composite estimate from multiple dates. For each model, a composite profile is created by calculating a point-wise average over selected dates (six for French Guiana and four for Gironde). In this section, we compare the composite estimates of W-DSPEB, C-DSPEB, and S2 Shores, and further detail is provided in Appendix B, including the point-wise absolute errors of the final estimates as well as the point-wise standard deviation of each method's single date estimates. Figure 9 presents the composite estimate of each of the models at French Guiana (top) and Gironde (bottom). Figure 8: Single-date estimation comparison of—from left to right—S2 Shores, C-DSPEB and W-DSPEB in French Guiana and Gironde. (**a–c,d–f**) show the correlations and point-wise absolute errors in French Guiana; (**g–i,j–l**) show the correlations and absolute errors in Gironde. Compared to S2 Shores and C-DSPEB, W-DSPEB achieves the lowest RMSE score over the entire bathymetry profiles in both test sites when a composite profile is considered. W-DSPEB also achieves a similar correlation to the S2 Shores model on the French Guiana site and a much higher correlation on the Gironde site. We note that the use of a composite estimate appears to reduce outliers with high error in the two deep learning methods, but not in S2 Shores. We assume that this is due to the batched training of the deep learning methods which tend to improve the average estimate of the models over multiple dates, as previously mentioned. All three methods, including S2 Shores, benefit from a composite estimate over multiple dates rather than a single-date estimate. The composite results of the three methods are analyzed further in Table 1.  
Table 1 shows that when using composite estimates, W-DSPEB outperforms S2 Shores on almost all metrics for the two sites (correlation, RMSE, and standard deviation over individual estimates). On two metrics, it is slightly worse but competitive with S2 Shores: W-DSPEB has a correlation of 0.91 in French Guiana compared to 0.93 for S2 Shores, and it has a slightly higher standard deviation over the 4 estimates from different dates in Gironde (4.01 versus 3.89). We note that W-DSPEB has an overall low temporal STD, which is averaged over the entire area, even in Gironde where single date estimates had high error. Compared to the wave kinematics-based methods, we observe a higher temporal variance from the color-based method C-DSPEB. In Figure 10, the sensitivity of C-DSPEB to background color change is evident as the prediction is highly influenced by turbidity. This \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Site** & **Metric** & **S2 Shores** & **C-DSPEB** & **W-DSPEB** \\ \hline \multirow{3}{*}{French Guiana} & r & 0.93 & 0.89 & 0.91 \\  & RMSE (m) & 3.63 & 3.96 & 3.26 \\  & Temporal STD (m) & 3.99 & 6.23 & 3.49 \\ \hline \multirow{3}{*}{Gironde} & r & 0.62 & 0.71 & 0.86 \\  & RMSE (m) & 6.46 & 7.59 & 5.12 \\ \cline{1-1}  & Temporal STD (m) & 3.89 & 6.13 & 4.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the composite estimates for the three methods. Temporal STD refers to the standard deviation over estimates of the same area from different dates. Figure 9: Composite estimation correlation comparison of S2 Shores (**left**), C-DSPEB (**middle**), and W-DSPEB (**right**) in French Guiana (**a–c**) and Gironde (**d–f**). variance due to turbidity has been noted in other deep learning approaches [39]. While other color-based methods may account for this variance, we consider it a strong argument for W-DSPEB over C-DSPEB. When using the DSPEB methods to estimate bathymetry over a large area, as seen in Figure 11, we note the stability of the W-DSPEB method. This correctly predicts water depth around the coastline and up to 35 m of depth.