## 4 Conclusions  
We studied the optimal interpolation method for regional MDT recovery based on GOCE-derived GGMs and mean sea surface. In particular, the performances of different GGMs in MDT recovery were studied, and the contributions introduced from the recently released GOCE-derived GGMs were quantified and assessed. Moreover, the choice of MSS model was investigated, and the effects on MDT modeling introduced from different MSS models were quantified. In addition, we compared the traditionally used Gaussian filtering method with the optimal interpolation method in regional MDT modeling. The numerical results over the Kuroshio showed that:  
1. The use of the recently released GOCE-derived GGM improved the accuracy of the computed MDT. The RMS of the difference between the MDT derived from sixth-generation GOCE-derived GGM modeled by the direct approach and independent ocean data was reduced by a magnitude of 5.4 mm (2.4 mm), compared to the result derived from the fourth-generation (fifth-generation) model. 2. The choice of recently published MSS models may have had limited effects on MDT recovery. The RMS of the difference between the MDT modeled from DTU18 MSS and ocean data was only 0.7 mm lower than that computed from DTU15 MSS. 3. For further comparison, the buoy data was introduced, and the geostrophic velocities derived from DTU18 MSS and different GOCE-derived GGMs were compared with the buoy data. The results revealed that the RMS of the differences between the zonal (meridional) velocities derived from the sixth-generation GGM and buoy data were 1.2 mm/s (1.8 mm/s) less than that derived from the fifth-generation model, and 2.2 mm/s (3.5 mm/s) less than the fourth-generation GGM, respectively. This also suggested that the improvements in the GGM could contribute to the accuracy improvement of the MDT modeling. 4. Moreover, the numerical experiments showed that the optimal interpolation method outperformed the Gaussian filtering approach, in which the geostrophic velocity derived from the optimal interpolation method had a smaller misfit against the buoy data by a magnitude of 10 mm/s (17 mm/s) when the zonal (meridian) component was validated. This was mainly due to the optimal interpolation method using the error information of the input data, which may have obtained more reasonable weights of observations than the Gaussian filtering method. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**MDT Solutions** & **Geostrophic Velocity** & **Min** & **Max** & **RMS** \\ \hline \multirow{2}{*}{DTU18 DIRR4-MDT} & u & \(-692.3\) & \(654.7\) & \(124.8\) \\  & v & \(-629.7\) & \(511.7\) & \(97.2\) \\ \multirow{2}{*}{DTU18 DIRR5-MDT} & u & \(-698.5\) & \(646.8\) & \(123.8\) \\  & v & \(-629.3\) & \(510.4\) & \(95.5\) \\ \multirow{2}{*}{DTU18 DIRR6-MDT} & u & \(-695.6\) & \(648.3\) & \(122.6\) \\  & v & \(-620.6\) & \(510.9\) & \(93.7\) \\ \multirow{2}{*}{GF-R4-MDT} & u & \(-707.7\) & \(766.6\) & \(133.4\) \\  & v & \(-675.9\) & \(651.6\) & \(119.3\) \\ \multirow{2}{*}{GF-R5-MDT} & u & \(-727.4\) & \(765.0\) & \(133.0\) \\  & v & \(-608.8\) & \(641.3\) & \(113.7\) \\ \multirow{2}{*}{GF-R6-MDT} & u & \(-722.6\) & \(763.9\) & \(132.9\) \\  & v & \(-622.9\) & \(637.2\) & \(110.8\) \\ \hline \hline \end{tabular} Note: the mean values of the misfit of the geostrophic velocity between the buoy data and the MDT models are removed.  
\end{table} 
Table 8: Statistics of the differences in the geostrophic velocities between the buoy data and the information deduced from the MDT solutions (units: mm/s). **Author Contributions:** Conceptualization, [PERSON] and [PERSON]; methodology, [PERSON] and [PERSON]; software, [PERSON] and [PERSON]; validation, [PERSON], [PERSON] and H.S. ; formal analysis, [PERSON] and [PERSON]; investigation, [PERSON]; resources, [PERSON]; data curation, [PERSON]; writing--original draft preparation, [PERSON] and H.S. ; writing--review and editing, [PERSON], H.S. and X.H. ; visualization, [PERSON]; supervision, [PERSON]; project administration, [PERSON]; funding acquisition, Y.W.