# Evaluation of the Consistency of Three GRACE Gap-Filling Data
## 2 Materials and Methods
### Consistency Analysis in the Spatial Domain  
Here we scrutinized these three datasets in the spatial domain and evaluate their differences. Similar to Section 3.1, we also compared the three datasets over the three periods: The end of GRACE (January 2016-June 2017), the gap months between the GRACE and GFO missions (July 2017-May 2018), and the beginning of GFO (June 2018-December 2018). Considering that the resolution of QF is approximately 1000-2000 km, we only compared the EWH results for SHCs truncated to degree 12. The GIA effect was also not considered here. Figure 5 shows the spatial distributions of rRMS among the IGG, SSA, and QF results. Recall that two series are correlated when the rRMS is less than 1.0 and implies a greater consistency. In most regions, the rRMS values of the three datasets are less than 1.0, indicating good consistency. In view of the scarcity of ground-truth data, the measurement-based QF can be treated as an approximately true value during the gap months. According to the statistical analysis in Figure 6, the rRMS values among IGG, SSA, and QF were approximately the same over the three periods, with approximately 60% less than 0.5 and approximately 85% below 1. The consistency of the statistical results further validates the reliability of the three gap-filling datasets. Actually, the rRMS values between SSA and IGG are concentrated in the 0-0.5 range and are slightly higher than those of IQ and QS, indicating a high consistency between SSA and IGG. The main reason may be that both of these two approaches are based on GRACE data. The SSA, IGG, and QF results are generally consistent but significant differences are found in some areas. Next, we chose six sites with large rRMS values (close to or greater than 2) in Figure 5 and compared their EWH time series. The six sites (a-f) were examined in terms of correlation and RMS of the EWH series in Figure 7. Panels a, b, c, and d of this figure plot the results over the entire period, the end of GRACE, the gaps between GRACE and GFO, and the beginning of GFO, respectively. IGG, SSA, and QF series are well correlated at sites b and d, with all correlation coefficients exceeding 0.76. There is no significant difference between the RMS values of SSA and QF, but the RMS values of IGG are greater than those of SSA and QF, which is particularly evident in the gap months (Figure 7c). That is, the signal recovered from IGG might be higher than from SSA and QF, but there is a good agreement in the seasonal variation of QF, SSA, and IGG. It can also be concluded that the correlation between QF and SSA is greater than the correlation between QF and IGG, except for sites e and f. Considering that QF is purely derived from satellite observations, we find that SSA shows better agreement with the observation-based results than IGG. In contrast, at sites with small RMS values, which means weak hydrological signals, such as those less than 5 cm, there was a large difference between the three datasets. Both the RMS and correlation coefficients are divergent, especially in sites a and e. Thus, we suggest that these three gap-filling data should be cautiously used in regions with weak hydrological signals. Figure 5: Worldwide comparison of the SSA, IGG, and QF results during **(a–c)** January 2016 to June 2017, **(d–f)** July 2017 to May 2018, and **(g–i)** June 2018 to December 2018. Plotted are the rRMS values of IGG relative to QF (subplots **(a,d,g)**), IGG relative to SSA (subplots **(b,e,h)**) and QF relative to SSA (subplots **(c,f,i)**). Figure 6: Probability distributions of Figure 4. Subplots **(a,c,e)** display the probabilities of rRMS values of IGG relative to QF (IQ), IGG relative to SSA (IS), and QF relative to SSA (QS), respectively, during three periods: January 2016 to June 2017, July 2017 to May 2018, June 2018 to December 2018. Subplots **(b,d,f)** display the cumulative probabilities of **(a,c,e)**, respectively. In summary, in most regions, the global terrestrial EWH results based on the degree-12 SHCs are highly consistent.