# Evaluation of the Consistency of Three GRACE Gap-Filling Data
## 2 Materials and Methods
### Global Mean Sea Level Change  
The global sea level change (measured by satellite altimetry) consists of the changes in sea mass (measured by GRACE) and density (i.e., steric change, measured by Argo floats). The consistencies among these three observations provide a possible way to evaluate the data quality of the GRACE gap filling products, since the other two datasets do not suffer from discontinuities. Figure 8 compares the time series of the global mean sea level anomalies calculated from the IGG and SSA data. The altimetry data, provided by the Commonwealth Scientific and Industrial Research Organization (CSIRO, [[http://www.cmarc.csiro.au/sealevel/sl_data_cmar.html](http://www.cmarc.csiro.au/sealevel/sl_data_cmar.html)]([http://www.cmarc.csiro.au/sealevel/sl_data_cmar.html](http://www.cmarc.csiro.au/sealevel/sl_data_cmar.html)), Canberra, Australia, April 2022), combine the data of TOPEX/Poseidon, Jason-1, Jason-2, and Jason-3 and are corrected for the inverse barometer and GIA effects. The monthly gridded 1\({}^{\circ}\)\(\times\) 1\({}^{\circ}\) Argo data were provided by the Scripps Institution of Oceanography [49]. The GIA effect in the QF, IGG, and SSA observations was also corrected using a three-dimensional GIA model [50]. The ocean-atmosphere model (GAD) was reintroduced into the GRACE SHCs, and the time-varying component of the monthly average atmospheric mass over the ocean was eliminated to account for the inverse barometer effect. Furthermore, all the time series were constructed using an ocean mask, which excludes coastal areas within 300 km. To calculate the ocean  
Figure 7: Comparison of correlations and RMS values at six sites with large differences in their rRMS values (see Figure 6 for locations). The analysis was performed over four time periods: (**a**) January 2003 to December 2018; (**b**) January 2016 to June 2017; (**c**) July 2017 to May 2018; (**d**) June 2018 to December 2018. IQ, IS, and QS represent the correlations between IGG and QF, IGG and SSA, and QF and SSA time series, respectively. The bars and series represent the RMS values and correlation coefficients, respectively. water mass, QF was truncated to degree 12 (Section 3.1), but the full spectrum (degree 60) of IGG and SSA was used. Figure 8a shows the seawater mass changes estimated from QF, IGG, and SSA, and the mass changes derived from the difference between Altimetry and Argo. The series is highly consistent over the entire period (January 2004 to December 2019). The correlations among QF, IGG, and SSA are all above 0.95, and the rRMS values between the three are all below 0.5. For instance, the rRMS value of IGG relative to SSA is just 0.15. After 2016, the seasonal variations in the three series remained consistent but they gradually departed from the Altimeter-Argo series. Notably, the SSA and IGG estimates of seawater quality were significantly lower than the Altimetry-Argo estimates at the beginning of 2017, but then there was an anomalous increase in IGG that mostly compensated for this difference, resulting in a great seasonal variation in 2017. In terms of annual variation, IGG results tend to be higher than SSA, QF, and Altimeter-Argo (Figure 8b). This difference is particularly significant in the 11-month gap, where the difference between IGG and SSA reached 7.8 mm. In contrast, the SSA results are generally consistent with the annual variation of Altimetry-Argo. Next, we scrutinized the discrepancies after 2016. The interannual variations were obtained by averaging the series over a sliding 12-month window (Figure 8a) and they were shifted upwards by 2 cm for better visualization. Figure 8a shows that all the IGG + Argo, SSA + Argo, and IGG + Argo series fit well with the altimetry series before August 2016. Figure 8: Comparisons of time series of global sea level anomalies. (**a**) Global mean sea level anomalies. QF, IGG, and SSA represent the seawater mass changes and Altimetry-Argo is the altimetry result minus the steric sea level change (note that seasonal signals remain in these data).