# Combination Analysis of Future Polar-Type Gravity Mission and GRACE Follow-On
## 3 Results and Analysis
### One-Year GFO-combined Model Series of FPG-89 and FPG-91  
In view of FPG-87 and FPG-93's deficiencies in zonal SHC determination, we therefore choose FPG-89 and FPG-91 in further GFO-joint gravity model recovery for the entire year 2006. We produce 12 monthly GFO-KBR & FPG models for FPG-89 and FPG-91, respectively. Monthly wRMS values of their global SDPs are demonstrated in Figure 7. As expected, GFO-KBR & FPG-91 outperforms the GFO-KBR & FPG-89 for its lower wRMS values over the whole year. Furthermore, we can observe slight variations in wRMS values of GFO-KBR & FPG-91 and GFO-KBR & FPG-89 models from month to month. Therefore, April and October are selected for further illustrations with corresponding results plotted in Figure 8.  
Figure 6: Global spatial differences plots (SDP) of different GFO-KBR & FPG combined models in January 2006: (**a**) GFO-KBR & FPG-87; (**b**) GFO-KBR & FPG-89; (**c**) GFO-KBR & FPG-93; and (**d**) GFO-KBR & FPG-91. Figure 8: True monthly HIS signal spatial plots and global spatial differences plots (SDP) of GFO-KBR & FPG-89 and GFO-KBR & FPG-91 in April and October 2006: (**a**) HIS signal in April; (**b**) HIS signal in October; (**c**) SDP of GFO-KBR & FPG-89 in April; (**d**) SDP of GFO-KBR & FPG-89 in October; (**e**) SDP of GFO-KBR & FPG-91 in April; (**f**) SDP of GFO-KBR & FPG-91 in October. Figure 7: Monthly latitude-weighted root mean square (wRMS) of global spatial differences plots (SDP) for GFO-KBR & FPG-89 and GFO-KBR & FPG-91 in 2006. On a global scale, results in April and October are plotted in the left and right columns of Figure 8, respectively. Subfigures in the top row represent the spatial signal plots of monthly true HIS signals, which are created the same way as SDP except that the \((\Delta C_{Im},\Delta S_{Im})=(\overline{C}_{Im}^{HIS},\overline{S}_{Im}^{HIS})\) in Equation (14); The middle and bottom rows represent SDPs of GFO-KBR & FPG-89 and GFO-KBR & FPG-91, respectively. As shown, the GFO-KBR & FPG-91 apparently suffers less from the temporal aliasing errors, especially in low- and medium-latitude areas. The error reductions in these areas are beneficial to the scientific study of global water cycle since the world's major river basins (e.g., the Amazon and Yangtze Rivers), as well as the majority of oceans, are located in the low and medium latitudes. On a regional scale, yearly-average wRMS of GFO-KBR & FPG-89 and GFO-KBR & FPG-91 are respectively calculated based on their regional SDPs. The regions that we select basically represent typical basins in low, medium, and high latitudes as marked in Figure 9. Besides, the ocean and land areas are also separately analyzed. As listed in Table 5, the superiority of GFO-KBR & FPG-91 over GFO-KBR & FPG-89 is mainly presented in the low- and medium-latitude regions, including the Amazon basin, North Murray-Darling basin and North China Plain (NCP). The last column of Table 5 shows ERR of GFO-KBR & FPG-91 over GFO-KBR & FPG-89 in terms of regional wRMS by setting \(q_{i}=wRMS_{\text{GFO-KBR \& FPG-91}}^{\Omega}\) and \(q_{j}=wRMS_{\text{GFO-KBR \& FPG-89}}^{\Omega}\) in Equation (16). It demonstrates that the GFO-KBR & FPG-91 reduces about 22% errors in ocean and 17% in land areas with respect to GFO-KBR & FPG-89. However, ERR mainly decreases with higher latitude and is even negative in the Greenland. The series of GFO-LRI & FPG-89 and GFO-LRI & FPG-91 models are not demonstrated here because of their indistinctive differences in spatial domain. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Area** & **wRMS of GFO \&** **wRMS of GFO \&** **GFO \&** **RFG \& FPG-91 Error** \\  & **FPG-89 (cm)** & **FPG-91 (cm)** & **Reduction Rate (\%)** \\ \hline Amazon & 2.76 & 1.98 & 28.3 \\ North Murray–Darling & 3.56 & 2.54 & 28.7 \\ Yangtze & 2.63 & 2.32 & 11.8 \\ NCP & 3.19 & 2.89 & 9.4 \\ Greenland & 1.01 & 1.15 & -13.9 \\ Ocean & 3.09 & 2.41 & 22.0 \\ Land & 2.53 & 2.09 & 17.4 \\ \hline \hline \end{tabular}
\end{table}