# Evaluation of the Consistency of Three GRACE Gap-Filling Data
## 2 Materials and Methods
### Fusion Method Based on Triple-Collocation
In contrast, at the end of GRACE, the statistics of rRMS values for IGG are comparable to the other two datasets. However, in the early GFO and the gap periods, only approximately 75% of IGG's rRMS values are less than 1, a bit lower than the other two datasets. The main reason for this discrepancy may be that the IGG recovers the time-varying gravity fields from the SLR using only GRACE data from February 2002 to August 2016 [16]. Note that both the QF time-varying gravity field solutions also incorporate the Swarm solutions (Table 1). SSA is a purely data-driven approach that fully inherits from GRACE/GFO observations, so its result generally reflects the consistency between GRACE and Swarm datasets. It is worth noting that there may be certain differences among SSA, IGG, QF, and Swarm coefficients with rRMS values less than 1. Figure 2 shows some examples in detail, including consistent or inconsistent series. The values on the top left are the RMS values for IGG, SSA, QF, and Swarm, respectively. As shown in Figure 2, the RMS values for  
Figure 1: rRMS values of the SHCs on the d/o plane (\(2\leq 1\leq 11\)) between the three datasets and Swarm datasets over three time periods: (**a–c**) End of GRACE (January 2016–June 2017), (**d–f**) the 11-month gap (July 2017–May 2018), and (**g–i**) beginning of GFO (June 2018–December 2018). The number of rRMS values in different intervals is annotated. The color scale is shown in subplot a.  
the coefficients of C\({}_{3,0}\), S\({}_{3,1}\), C\({}_{5,0}\), and C\({}_{6,0}\) are roughly comparable. Although the Swarm SHCs time series exhibits higher volatility than the others, especially before mid-2015, the SHCs of IGG, SSA, QF, and Swarm are essentially consistent on average. The consistency deteriorates when the seasonality is weak, e.g., C\({}_{2,1}\) and C\({}_{4,0}\). Another possible reason for the discrepancies is, as discussed in [PERSON] et al. (2020) [15], the different mean pole models [43] used between GRACE and Swarm solutions. Furthermore, compared to QF, it is noticeable that there is better consistency between IGG and SSA (Figure 2a,d). The main reason for this may be that both SSA and IGG data are highly inherited from GRACE/GFO. Next, we calculated the degree variance of the SHCs (degree 5-60) of the IGG, QF, and SSA data during the 11-month gap (July 2017 to May 2018) between GRACE and GFO (Figure 3), which illustrates the signal intensity of each degree term of the SHCs. The variances of the SHCs of the IGG and SSA data gradually decrease with an increasing degree and show a fairly consistent trend. The variances of the lower-degree terms of the QF coefficients (\(l\leq 12\)-16) are essentially consistent with those of SSA and IGG, but the variances of the higher-degree terms of QF progressively increase with an increasing degree, indicating a rapid increase in the noise level. This phenomenon is mainly attributable to the limited observational techniques and spatial resolution of QF [13; 31]. Therefore, with spatial resolution accuracy much lower than GRACE, QF is only suitable for monitoring large-scale mass transport (1000-2000 km). The degree variance in IGG is slightly larger than in SSA, especially for coefficients with degrees > 40 and for the September 2017 result (Figure 3c). In other words, the signal intensity in SSA is slightly smaller than in IGG. Figure 2: Time series of selected coefficients of the IGG, SSA, QF, and Swarm data: (**a**) C\({}_{2,1}\), (**b**) C\({}_{3,0}\), (**c**) S\({}_{3,1}\), (**d**) C\({}_{4,0}\), (**e**) C\({}_{5,0}\), (**f**) C\({}_{6,0}\). The upper left values are the RMS values for IGG, SSA, QF, and Swarm, respectively.