## 2 Data and Methods  
GRACE L2 RL05 and RL06 monthly gravity field solutions were published by the Center for Space Research (CSR) at the University of Texas at Austin [26; 27], GFZ [28; 29] and the Jet Propulsion Laboratory (JPL) at the California Institute of Technology [30; 31]. All the solutions are provided as fully normalized spherical harmonics with degree and order up to at least 60. In order to ensure the proper scientific applications of GRACE monthly gravity field solutions, some appropriate corrections associated with degree one terms, \(C_{20}\), and glacial isostatic adjustment (GIA) are routinely applied. For GRACE RL06 data, some recent studies adopted the GSFC \(C_{30}\) product in TN14 instead of GRACE-determined \(C_{30}\)[15; 16]. In this study, we only calculate mass variations caused by degree one terms (for each data processing center), SLR-based \(C_{20}\) estimates, and GSFC \(C_{30}\), as well as GRACE-determined \(C_{30}\) estimates. As provided in Table 1, to assess the influence of degree one terms on polar ice sheet mass variations, monthly estimates of degree one terms based on the optimized method by [24] in two versions, namely SUN11 and SUN14, and those improved estimates (SV) published by [25], are analyzed for GRACE RL06 data from each data processing center. To compare the impact of degree one terms on polar ice sheet mass variations derived from GRACE RL05 data with that obtained from GRACE RL06 data, monthly estimates of degree one terms (SW) determined by [23] at the University of South Florida are also adopted. SLR-based \(C_{20}\) solutions corresponding to GRACE L2 RL05 and RL06 data are separately analyzed during the GRACE mission span. For GRACE RL05 data, SLR-derived \(C_{20}\) estimates were available in GRACE TN07 [11]. For GRACE RL06 data, SLR-based \(C_{20}\) estimates in two versions, namely \(C_{20}\) estimates derived from SLR only and those obtained from the combination of GRACE and SLR, are separately provided in GRACE TN11 [7] and TN14 [13]. Besides, SLR-based \(C_{20}\) solutions, newly published by [17] (referred to as GFZ-SLR) at GFZ, are also utilized. In addition, the potential influence from \(C_{30}\) is also studied, and GRACE-determined \(C_{30}\) in RL05 and RL06 data from each data processing center and GSFC \(C_{30}\) in GRACE TN14 since March 2012 are separately analyzed. We conduct four experiments to derive mass variations caused by these low degree spherical harmonic coefficients separately over the GrIS and the AIS: 1) only degree one terms corresponding to GRACE RL05 and RL06 data are utilized to compute mass variations; 2) only SLR-based \(C_{20}\) estimates from TN07, TN11, TN14, and GFZ are separately used to calculate mass variations; 3) only GRACE-determined \(C_{30}\) in RL05 and RL06 data and SLR-based \(C_{30}\) in TN14 are used to compute \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Data Used** & **Degree One Terms** & **\(\mathbf{C_{20}}\)** & **\(\mathbf{C_{30}}\)** \\ \hline GRACE RL05 & SW & TN07 & GRACE \\ (CSR/GFZ/JPL) & & & \\ \hline GRACE RL06 & SUN11, SUN14, SV & TN11, TN14, GFZ-SLR & GRACE, \\ (CSR/GFZ/JPL) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The data sets adopted in this study. Only auxiliary data including degree one terms, satellite laser ranging (SLR)-based \(C_{20}\) and Gravity Recovery and Climate Experiment (GRACE)-determined \(C_{30}\) estimates separately corresponding to GRACE RL05 and RL06 data (from each data processing center) are analyzed during the GRACE mission span. Besides, SLR-based (GSFC) \(C_{30}\) estimates since March 2012 are also utilized. Note that the following abbreviations are used: TN—GRACE Technical Note; SW—degree one terms from [23]; SUN11—degree one terms from [24], with \(C_{20}\) estimates in TN11 used; SUN14—degree one terms from [24], with \(C_{20}\) estimates in TN14 used; SV—degree one terms from [25], with \(C_{20}\) estimates in TN14 used; GFZ-SLR—\(C_{20}\) estimates from [17]; GSFC—the Goddard Space Flight Center.