# Evaluation of the Consistency of Three GRACE Gap-Filling Data
## 2 Materials and Methods
### Comparison with Water Storage Model  
Here, we adopted a climate-driven water storage change model (GRACE-REC) provided by [PERSON] (2019) [54] to test the ability of the gap-filling products to recover hydrological signals. Due to the low resolution of the QF dataset, we ignored it in our analysis here.  
Figure 9 compares the RMS values of residuals of IGG and SSA by subtracting the GRACE-REC model for results between July 2017 and May 2018. The difference between the gap-filling data and the model values may include unmodeled signals and the model deficiency (which is assumed to be small). Figure 9a,b shows the spatial distribution of the RMS values, where values less than 1 indicate two datasets are in some way consistent. As shown in Figure 10d, SSA has a higher proportion of relative RMS values smaller than 1 than IGG (65% versus 59%). Moreover, the spatial distribution results in Figure 9a,b show that the IGG was significantly wider than the SSA for regions with relative RMS values greater than 1. Therefore, we conclude that the SSA gap-filling series is more consistent with GRACE-REC than with IGG and shows better performance in restoring transient hydrological events.  
Figure 10 shows the time series of EWH and precipitation at points A, B, C, and D (marked in Figure 9), where the relative RMS values are large, to illustrate the potential bias in IGG and SSA. The precipitation data are the monthly average reanalysis data, expressed as EWH, obtained from the Climate Data Store ([[https://cds.climate.opernicus.eu/#](https://cds.climate.opernicus.eu/#)]([https://cds.climate.opernicus.eu/#](https://cds.climate.opernicus.eu/#))!/home, Brussels, Belgium, April 2022). The water storage in point A shows a 2010 drought and a post-2016 increase, which are consistent with the progression of dry and wet periods. The alternation of positive and negative water storage anomalies is well-reflected by the SSA and GRACE-REC results, but not in the IGG results. This case demonstrates that using the first six modes in IGG may lose some interannual variation in regional signals. This problem can also be found at point C, where the IGG result fails to capture the water storage after 2016 due to the contemporaneous increase in precipitation. The time series of IGG and SSA at points B, C, and D are fairly consistent until 2017, after which their differences start to increase. The main reason for this discrepancy may be that the IGG only used GRACE data from February 2002 to August 2016, but the extrapolated gravity fields from the SLR could not maintain the previous variation pattern and may not accurately reflect some sudden mass change signals as GRACE does. The series of SSA and GRACE-REC were mostly consistent, especially before and after the gap period. However,  
the SSA data have one big shortcoming. As it is totally data-driven, it cannot capture a suddenly emergent climatic event during the data gap. For instance, point D located in North America was influenced by a sudden precipitation deficit in 2016, resulting in GRACE-REC results showing a sharp decrease in water storage. However, SSA reflects only a moderate decrease in water storage in 2016. Nevertheless, such interannual variability is absent in the IGG result as well.  
Figure 9: Comparison of the RMS values of residuals of (**a**) IGG and (**b**) SSA by subtracting GRACE-REC. (**c**) Probability and (**d**) cumulative distribution of grid values in (**a**,**b**).  
Figure 10: Time series of EWH and precipitation at points A, B, C, and D (marked in Figure 9): (**a**) point A, (**b**) point B, (**c**) point C, (**d**) point D. The red curve in the precipitation plots is the smoothed result of a 12-month sliding window applied to the monthly precipitation (gray bars).