## 3 Results  
We first compare the mass change time series computed from degree one terms separately corresponding to GRACE RL05 and RL06 data over each ice sheet (experiment 1), as depicted by Figure 2. It is obvious that these time series of mass change caused by degree one terms all exhibit significant annual variations together with a negative linear trend for the GrIS (Figure 2a) but a positive trend for the AIS (Figure 2b). Over the GrIS, annual peaks occurred in March/April/May and minima typically appeared in August/September/October. In contrast, annual peaks appeared in August/September/October over the AIS, with minima occurring in March/April/May. Apparent discrepancies can be seen among mass change time series derived from degree one terms corresponding to GRACE RL05 and RL06 data. For instance, mass change time series caused by degree one terms (SW) corresponding to GRACE RL05 data (blue lines in Figure 2) show smaller annual amplitudes and a more moderate linear trend than those for GRACE RL06 data (red, green, and black lines) over each ice sheet. All the mass change time series derived from SUN11, SUN14, and SV are in better agreement with each other. As listed in Table 2, mass variations caused by degree one terms (SW) corresponding to GRACE RL05 data show a linear trend of \(-2.6\pm 0.2\) Gt/yr and \(13.1\pm 0.8\) Gt/yr over the GrIS and the AIS, respectively, with respective annual amplitudes of 25.8 Gt and 122.1 Gt. For GRACE RL06 data, the trends of mass variations caused by degree one terms (SUN11) over the GrIS and the AIS are from \(-6.7\pm 0.2\) Gt/yr to \(-7.1\pm 0.2\) Gt/yr and from \(35.8\pm 1.0\) Gt/yr to \(37.5\pm 0.9\) Gt/yr, respectively, which in absolute value is 2.5 times larger than that for GRACE RL05 data. The annual amplitude of mass change caused by degree one terms corresponding to GRACE RL06 data is more than 30% larger than that over each ice sheet for GRACE RL05 data. Mass variations caused by degree one terms (SUN14) and those (SV) provided by [25] agree well with those derived from degree one terms (SUN11) over each ice sheet (Table 2 and Figure 2). Degree one terms (SUN14) modify the trend of mass variations by\(-0.4\pm 0.3\) Gt/yr and \(2.4\pm 1.4\) Gt/yr over the GrIS and the AIS, respectively, as compared to SUN11. Mass variations computed from SV show the most negative and the most positive mass trends together with a relatively smaller annual amplitude over the GrIS and the AIS, respectively, as compared to those derived from SUN11 and SUN14. Figure 2: Time series of mass change caused by degree one terms (geocenter motion, GEOC) over (**a**) the GrIS and (**b**) the AIS, respectively, using degree one terms corresponding to GRACE RL05 and RL06 data published by each data processing center. CSR/GFZ/JPL indicates that the time series of mass change caused by degree one terms are calculated separately and are shown for GRACE data published by the Center for Space Research (CSR), Deutsches Geo Forschungs Zentrum (GFZ), and Jet Propulsion Laboratory (JPL). To understand the impact of SLR-based \(C_{20}\) estimates on mass variations of polar ice sheets, we compute mass variations over the GrIS and the AIS by only using SLR-based \(C_{20}\) estimates during the GRACE mission span (experiment 2). As shown in Figure 3, mass variations caused by SLR-based \(C_{20}\) estimates corresponding to GRACE RL05 and RL06 data are generally consistent with each other. Significant annual variations with a similar phase can be visible from all these mass change time series. Mass variations caused by \(C_{20}\) estimates from TN07, TN11, and GFZ exhibit better agreement on the annual amplitude. A smaller annual amplitude can be seen from mass variations derived from \(C_{20}\) estimates in TN14. As shown in Table 3, the annual amplitude of mass variations derived from \(C_{20}\) estimates in TN14 is 25% smaller than those corresponding to TN07, TN11, and GFZ.