# Next-Generation Gravity Missions: Sino-European Numerical Simulation Comparison Exercise
## 4 Results and Discussions
Another issue to mention in the error standard deviations is the transition at harmonic degree 15, which is related to the maximum degree of the daily co-parameterization, which is slightly visible in the IGG-CAS formal errors (Figure 7b), while the other four solutions show a very smooth transition. Analyzing the error estimates of the low-degree SH coefficients also reveals significant differences. The error estimates of the IGG-CAS (Figure 7b) and HUST (Figure 7e) solutions predict much lower errors of the low-degree components relative to the high-degree coefficients than the other solutions, which might indicate that the GPS-SST high-low component has been given a higher relative weight when combining the NEQs. In this sense, the analysis of the error estimates allows deeper insights into the gravity recovery strategies, leading, however, as discussed above to very comparable results in terms of SH coefficient retrieval. Figure 8a shows the global EHW field derived from the full AOHIS signal based on the ESA AOHIS model [19] (cf. Table 2) of the first 9-day period of Scenario A, and Figure 8b-f show EWH difference grids associated to the coefficient differences shown in Figure 6. These global grids have been evaluated up to the full SH resolution of d/o 70. All EWH difference fields show the typical striping pattern which is mainly resulting from residual temporal aliasing. The Tongji and TUM solutions show the lowest stripiness. In order to quantify these results, Table 4 provides an overview of the main statistical parameters of these EWH (difference) fields. Also here, the Tongji solution shows the smallest RMS deviation from the \"true\" AOHIS model, followed by the TUM result. Evidently, these statistics are dominated by the remaining high-frequency errors expressed by stripes in the EHW fields. Therefore, we re-do the analysis for fields resolved only up to SH d/o 30. According to Figure 5, at this degree the signal-to-noise ratio is safely above one for all five solutions. The results are shown in Figure 9 and Table 5. Please notice that the scale is reduced from 20 cm to 10 cm for the EWH (difference) fields. In this d/o 30 analysis, now the IGG-CAS solution performs best, followed by the results of TUM, WHU, and HUST. These three solutions are practically on the same error level. This is also consistent with the degree RMS results shown in Figure 5. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model (d/o 70)** & **Min (cm)** & **Max (cm)** & **RMS (cm)** \\ \hline AOHIS & \(-\)50.38 & 66.84 & 5.46 \\ TUM - AOHIS & \(-\)37.62 & 36.69 & 4.80 \\ IGG-CAS - AOHIS & \(-\)29.62 & 30.43 & 6.36 \\ Tongji - AOHIS & \(-\)31.46 & 26.71 & 3.91 \\ WHU - AOHIS & \(-\)31.97 & 32.58 & 5.41 \\ HUST - AOHIS & \(-\)40.68 & 29.56 & 6.11 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Main statistical parameters of EWH input and EWH difference fields up to SH d/o 70 of the first 9-day period of Scenario A.  
Figure 8: (**a**) Equivalent water heights (EWH) (cm) grid related to the input AOHIS model up to d/o 70, and EWH (cm) differences to this AOHIS model of the (**b**) TUM; (**c**) IGG-CAS; (**d**) Tongji; (**e**) WHU; (**f**) HUST solutions. Shown is the first 9-day period of Scenario A. As a general conclusion, at degree 30 the RMS variation among the five solutions is in the order of 10% of the total signal RMS. Solutions for other time periods show very similar behavior to the ones presented above, and are therefore not explicitly presented and discussed in this paper. As already mentioned in Chapter 3, all processing centers co-estimated daily gravity field parameters up to SH d/o 15 in order to reduce temporal aliasing effects. Figure 10 shows the resulting degree error RMS curves, which represent differences of daily estimates to the daily AOHIS \"true\" signals (black curve), averaged over the whole recovery period. Also here, the performance of these