## 4 Evaluation
### Gulf Stream
Last, when computing the radially averaged power spectra as a spatial domain averaged over the four 20-day validation period and the associated signal-to-noise ratio for joint use of along-track nadir with SWOT data (Figure 7b), we observe that AnDA and FP-GENN lead to a better constraint of the SSH spectrum compared to the actual OI capabilities. In particular, FP-GENN produces a spectrum closer \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & **Model Type** & **R-Score** & **I-Score** & **AE-Score** & **Model Type** & **R-Score** & **I-Score** & **AE-Score** \\ \hline \multirow{5}{*}{**GULFSTREAM**} & OI & 87.32 & 72.17 & – & \(\
abla_{\text{OI}}\) & 78.03 & 75.97 & – \\  & AnDA & 94.85 & 77.91 & – & \(\
abla_{\text{AnDA}}\) & **85.56** & 79.14 & – \\  & VE-DINEOF & **96.11** & 72.72 & – & \(\
abla_{\text{VE-DINEOF}}\) & 82.69 & 75.61 & – \\  & FP-ConvAE & 87.82 & 76.32 & 82.85 & \(\
abla_{\text{FP-ConvAE}}\) & 77.80 & 76.81 & 75.89 \\  & FP-GENN & 91.78 & **84.56** & 93.15 & \(\
abla_{\text{FP-GENN}}\) & 81.05 & **80.56** & 84.24 \\ \hline \multirow{5}{*}{**GULFSTREAM**} & OI & 93.25 & 74.25 & – & \(\
abla_{\text{OI}}\) & 73.83 & 75.78 & – \\  & AnDA & 96.05 & 83.55 & – & \(\
abla_{\text{AnDA}}\) & **89.89** & 82.88 & – \\  & VE-DINEOF & **97.13** & 75.28 & – & \(\
abla_{\text{VE-DINEOF}}\) & 88.19 & 76.69 & – \\  & FP-ConvAE & 80.63 & 77.51 & 83.26 & \(\
abla_{\text{FP-ConvAE}}\) & 76.20 & 76.49 & 75.84 \\  & FP-GENN & 96.49 & **90.13** & 95.58 & \(\
abla_{\text{FP-GENN}}\) & 86.96 & **85.33** & 88.23 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Sea surface height (SSH) and SSH gradient field R/I/AE-scores computed for the four 20-day non-continuous validation periods for OI, (post-)AnDA, VE-DINEOF, FP-ConvAE and FP-GENN for both nadir use only and joint assimilation/learning with wide-swath SWOT data. (**a**) Taylor diagram, (**b**) signal-to-noise ratio. Figure 7: Taylor diagram and signal-to-noise ratio computed for the four 20-day non-continuous validation periods for OI, (post-)AnDA, VE-DINEOF, FP-ConvAE and FP-GENN computed for both nadir use only and joint assimilation/learning with wide-swath SWOT data. (**a**) Taylor diagram, (**b**) signal-to-noise ratio. to the ground truth real spectrum, by catching up the submesoscale range up to 60 km (when picking up signal-to-noise ratio equals to 0.5) when considering a joint learning from along-track nadir and additional wide-swath SWOT data. Note on Figure 7b the importance of the patch-based AnDA post-processing to its performance which clearly appears on the spectra: its overestimation by the blocky patch-based AnDA rough outputs is partly mitigated thanks to the smoothing produced by averaging the patches overlapping areas. This result may certainly be further improved, for instance by training a CNN rather than using a simple average-based smoothing. To further enhance the vizualization of the improvements brought by the different interpolators, Figures 8 and 9 depict the spatial SSH gradient ground truth and its global reconstruction based on OL (post-)AnDA, VE-DINEOF, FP-ConvAE and FP-GENN with both single along-track nadir data and joint use with wide-swath pseudo-observations on 4 August 2013. In Appendix A, complementary Figures 10 and 11 are provided for the SSH on the same day. To support what has already been said through the performance analysis previously discussed, FP-GENN using 5-day accumulated nadir observations appears closer to the groud truth SSH field than the reconstruction obtained with FP-ConvAE using a similar solver but a simple auto-encoder representation of the dynamics. The latter clearly oversmoothes the true field and also exhibits some unnecessary artifacts far from the direct vicinity of the along-track and/or wide-swath data on the SSH gradient, thereby explaining the noisy-related small scale energies on the spectra. The same artifacts appear on the VE-DINEOF mapping which exhibits discontinuities between the known wide-swath-informed areas and the filled missing data.