## 3 Results
### Gravity Field Solutions
#### 3.3.2 Solutions estimated from 2.5 years of observations  
Finally, we extend GOCE data span to the period from November 2009 to July 2012 to compile the carrier phase, ESA-orbit, and Graz-orbit solutions up to degree and order 130. This data period is comparable with the one used in [PERSON] et al. (2015), and the gravity field model DGM-1S was also used as a reference model to access the quality of the obtained three gravity field solutions similar to [PERSON] et al. (2015). The model DGM-1S is based on data from the GRACE and GOCE satellite gravity missions ([PERSON] et al., 2017). Figure 6 depicts the DE-RMS of three solutions. Table 7 shows the cumulative geoid height differences w.r.t. DGM-1S for the degrees up to d/o 130. Figure 7 presents the spatial distribution  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Min** & **Max** & **Mean** & **RMS** \\ \hline Carrier phase solution & \(-0.469\) & \(0.201\) & \(3.531\times 10^{-3}\) & \(0.068\) \\ ESA-orbit solution & \(-0.360\) & \(0.331\) & \(1.001\times 10^{-2}\) & \(0.060\) \\ Graz-orbit solution & \(-0.728\) & \(0.261\) & \(5.091\times 10^{-3}\) & \(0.096\) \\ SGG-orbit solution & \(-0.365\) & \(0.187\) & \(1.251\times 10^{-3}\) & \(0.063\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Statistics of the geoid height differences (unit: m) w.r.t. EIGEN-6C4 with the 500 km Gaussian smoothing applied.  
Figure 5: Geoid height errors of the recovered spherical harmonic coefficients w.r.t. EIGEN-6C4 with the 500 km Gaussian smoothing applied.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Degree** & \begin{tabular}{c} **Carrier Phase** \\ **Solution** \\ \end{tabular} & \begin{tabular}{c} **ESA-Orbit** \\ **Solution** \\ \end{tabular} & \
\begin{tabular}{c} **Graz-Orbit** \\ **Solution** \\ \end{tabular} &
\begin{tabular}{c} **SGG-Orbit** \\ **Solution** \\ \end{tabular} \\ \hline
10 & 0.09 & 0.08 & 0.07 & 0.08 \\
30 & 0.67 & 0.65 & 0.48 & 0.71 \\
50 & 2.28 & 1.88 & 1.51 & 2.54 \\
70 & 5.50 & 4.43 & 4.70 & 6.32 \\
90 & 11.71 & 10.34 & 13.97 & 14.09 \\
110 & 21.98 & 21.30 & 26.68 & 26.28 \\
130 & 37.02 & 39.19 & 46.72 & 46.96 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Cumulative geoid height differences (unit: cm) w.r.t. EIGEN-6C4 up to different degrees.  
of the recovered gravity field solutions with the 500-km Gaussian smoothing filter applied. There are obvious systematic errors along the geomagnetic equator, especially for the solutions obtained from the orbit differentiation method, which is the same situation in [PERSON] et al. (2019).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Degree** & **Carrier Phase Solution** & **ESA-Orbit Solution** & **Graz-Orbit Solution** \\ \hline
10 & 0.07 & 0.05 & 0.03 \\
30 & 0.38 & 0.36 & 0.28 \\
50 & 1.08 & 1.01 & 0.97 \\
70 & 2.60 & 2.64 & 2.76 \\
90 & 5.58 & 6.02 & 6.57 \\
110 & 10.36 & 11.76 & 12.71 \\
130 & 17.70 & 21.43 & 22.11 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Cumulative geoid height differences (unit: cm) w.r.t. DGM-1S up to different degrees.  
Figure 6: DE-RMS of the recovered spherical harmonic coefficients w.r.t. DGM-1S.