# Evaluation of the Consistency of Three GRACE Gap-Filling Data
## 2 Materials and Methods  
### GRACE Products and Water Storage Estimates  
In this study, we investigated three GRACE gap-filling products (SSA, IGG, and QF) in the form of SHCs. Table 1 lists the satellites from which these data were derived. The SSA data were based on the GSM RL06 level-2 product from CSR truncated to degree 60, and the time span is from January 2003 to December 2020 [21]. The degree-1 terms were supplemented using the method of [PERSON] et al. (2016) [28], and the C20 term was replaced by the result of SLR [29]. The IGG data are truncated to degree 60 and the data time span is from January 2003 to June 2020 [16]. It was solved from SLR observations using empirical orthogonal functions (EOFs) from the GRACE solutions as the base functions. The time-varying gravity field of ITSG-Grace2018 (155 months, April 2002-August 2016 [30]) was used as a source of EOFs after replacing C20 by the result of SLR [29]. To mitigate the truncation effect of EOFs and ensure the stationarity of the signals outside the GRACE time frame, the high-degree and low-degree terms of the SHCs are estimated separately: The high-degree terms are estimated based on the leading modes in the EOF decomposition of the GRACE solutions, while the low-degree terms are inverted from the SLR observations [16]. Considering the different maximum degrees of SLR solutions estimated in IGG, [PERSON] and [PERSON] (2021) provided six combinations of time-varying gravity field models [16]. The first five of these models are listed in Table 2, and the sixth model is their weighted average (EnsMean). As mentioned in [PERSON] and [PERSON] (2021), whether focusing on the global or on regions with spatially homogeneous signals, EnsMean is a good compromise of the first five models, except for some limitations in Greenland [16]. Therefore, we adopt EnsMean hereafter. \begin{table}
\begin{tabular}{c c c} \hline
**Data Style** & **Satellite** & **Satellite Type** \\ \hline SSA & GRACE, GRACE-FO & Gravity \\ \hline IGG & Lageos \(\
icefrac{{1}}{{2}}\), AJISAI, Starlette, Stella & Geodetic SLR \\  & GRACE, GRACE-FO & Gravity \\ \hline \multirow{6}{*}{QF} & Champ, GRACE A/B, GOCE & Gravity \\  & Swarm A, B, C & Geomagnetic \\  & TanDEM-X, TerraSAR-X, Kompsat5, Sentinel 1A, 1B, 2A, 3A & SAR \\ \cline{1-1}  & SAC-C, CNOFS & Environmental \\ \cline{1-1}  & Cosmic 1-6, MetOpA, MetOpB & Weather \\ \cline{1-1}  & Jason 1-3 & Altimetry \\ \cline{1-1}  & Lageos \(\
icefrac{{1}}{{2}}\), LARES, Starlette, Stella, Larets, AJISAI, Beacon-C, & Geodetic SLR \\ \hline \end{tabular}
\end{table} 
Table 1: The HLSST LEO satellites, SLR, and low-low satellite-to-satellite tracking (LLSST) satellites used for obtaining the SSA, IGG, and QF data. The QF data constitute a series of monthly gravity field models with SHCs up to degree-and-order (d/o) 60. The data are based on HLSST tracking and SLR data provided by the International Centre for Global Earth Models. Nine SLR geodetic satellites and 27 low-earth orbiting (LEO) satellites are utilized in the computation, including four dedicated gravity satellites: CHAMP, GOCE, and GRACE A/B [27]. Details of these satellites are given in Table 1. The SLR and HLSST data are combined at the normal equation level using Variance Component Estimation, and their spatial resolution is approximately 1000-2000 km [13; 31]. The v2-Kalman filtered QF data, provided by [PERSON] (2019) [27], was used in this study, and the data time span is from January 2003 to December 2018. As the SHCs of the IGG and QF data do not contain degree-1 terms, we supplement the degree-1 terms of IGG and QF with these from [PERSON] et al. (2016) (same as SSA data) [28].