## 3 Results and Discussion  
### MDT Solutions from Different GOCE-Derived GGM  
In order to evaluate the performance of the MDT solution derived from different GOCE-derived GGM, the MDT with a spatial resolution of \(10^{\prime}\) and a reference time of 1993-2012 was solved, which combined the DTU18 MSS with the GOCE-derived GGMs, including the DIRR4, DIRR5, DIRR6, TIMR4, TIMR5, and TIMR6. The method for constructing MDT was the optimal interpolation method, which is described in detail above. The large-scale MDT was estimated by using the Gaussian filtering method with a 400 km filtering radius. The CNES-CLS18 MDT was used for estimating the variance and covariance of the MDT. Figure 3: The correlation radii in (**a**) zonal and (**b**) meridional of the study area. The MDTs solved by the OIM through the combination of the DTU18 MSS and GOCE-derived GGMs by means of the direct approach are shown in Figure 4, where Figure 4a-c are the MDTs based on the DIRR4, DIRR5, and DIRR6, denoted as DTU18 DIRR4-MDT, DTU18 DIRR5-MDT, and DTU18 DIRR6-MDT, respectively; while Figure 4d-f are the time-wise solutions, which are denoted as DTU18 TIMR4-MDT, DTU18 TIMR5-MDT, and DTU18 TIMR6-MDT, respectively. In order to verify the reliability of the MDT solutions, the reference MDT derived based on the average of the oceanographic and geodetic MDTs models; i.e., SODA, ORAS5, CNES-CLS13 MDT, and Copernicus, were used for comparison. However, the evaluations of the error levels of the four MDTs, in addition to the reference MDT, were needed. Thus, these models were first referenced to 1993-2016; that is, the same as the buoy data, and the corresponding geostrophic ocean current was deduced and then compared with the in situ data, as shown in Table 4. The results showed that the RMS of the difference between geostrophic current velocity derived from reference MDT and the buoy data was relatively smaller in comparison: 112 mm/s (91 mm/s) in the zonal (meridional) directions, respectively, which may be due to the smoothness of the noise. As a result, the reference MDT could be used for the comparative analysis in this study. The differences between the reference MDT and the estimated MDTs are shown in Figure 5. It can be seen that the differences between the MDT solutions by OIM and the reference MDT were mainly concentrated in the current region in Figure 1, while there were fewer differences between the filtered MDT and reference MDT in most regions. This may be because the MDT models also were calculated through the filtering procedure, which screened out some of the detailed signals and is therefore not evident in Figure 5. Table 5 shows the statistical results of these comparisons (the mean differences are removed). The RMS of the difference between the DTU18 DIRR6-MDT solution and reference MDT was 77.0 mm, which was 2.4 mm lower than that of the DTU18 DIRR5-MDT solution and 5.4 mm lower than that of the DTU18 DIRR4-MDT solution. In addition, the RMS of the difference between the DTU18 TIMR6-MDT and reference MDT was 0.5 mm (5.7 mm) lower than  
Figure 4: The estimated MDT based on (**a**) DIRR4, (**b**) DIRR5, (**c**) DIRR6, (**d**) TIMR4, (**e**) TIMR5, and (**f**) TIMR6. that of DTU18 TIMR5-MDT (DTU18 TIMR4-MDT), suggesting that the development of the GGM could contribute to the MDT modeling. The recently satellite-only GGM was derived from all of the available GOCE gravity gradiometry data and recalibrated satellite orbit data. This illustrated that the accumulation of GOCE data and updated data preprocessing methods can be beneficial for MDT recovery.