## 4 Discussion  
The accuracy of GRACE-derived ice sheet mass balance estimates is affected by many factors, such as the post-processing techniques used to remove the north-south stripes in the spatial domain, the uncertainty of the adopted GIA model, the influences from degree one and SLR-based \(C_{20}\) time series, and so on. Currently, the uncertainty of the GIA model has been recognized as the major source of uncertainty in ice mass balance. For instance, over the AIS, [32] pointed out that the uncertainties of six commonly used GIA models range from \(\pm 13\) Gt/yr to \(\pm 27\) Gt/yr. The contribution from low degree spherical harmonics was thought to have a non-negligible effect on GRACE-derived mass variations since the early stage of the GRACE mission. To date, the choice of these low degree spherical harmonics for accurately deriving ice sheet mass balance estimates is still an open issue: there are different approaches used to compute estimates of these low degree spherical harmonic coefficients, which could cause discrepancies among GRACE-derived ice mass balance estimates. Here, we select the AIS as an example region to demonstrate the influence of these low degree spherical harmonics on GRACE-derived ice mass variations. Table 7 provides mass balance estimates for the AIS reported by several previous studies, with the used data, the study period and the adopted low degree terms shown. In order to analyze the impact of low degree terms on ice mass balance estimates, we calculate the trend of mass variations caused by the respective degree one terms (including SW, SUN11, SUN14, and SV), and caused separately by SLR-based \(C_{20}\) during the corresponding study period over the AIS. Apparently, compared with the impacts of degree one terms corresponding to GRACE RL05 data, significantly increased influences can be found from these degree one terms corresponding to GRACE RL06 data on the AIS mass balance estimates. The increased influences are  
Figure 5: Mass change time series computed by the combination of degree one terms, SLR-based \(C_{20}\) estimates, and C\({}_{30}\) solutions corresponding to CSR/GFZ/JPL-published GRACE RL05 and RL06 data over (**a**) the GrIS and (**b**) the AIS during the GRACE mission span. CSR/GFZ/JPL means time series of mass change caused by the combination of degree one terms, SLR-based \(C_{20}\) and GRACE-determined C\({}_{30}\) estimates from CSR, GFZ, and JPL, are separately calculated and shown. primarily associated with the optimized processing choices in [24; 25] when estimating degree one terms, e.g., the truncation degree of GRACE gravity field solutions, the width of the buffer zone, and including self-attraction and loading effects. For GRACE RL06 data, it is obvious that differences among these three time series of degree one terms affect the AIS mass balance estimates by 3-6 Gt/yr, depending on the study period. SV-caused mass variations over the AIS show the most positive trend, while the SUN11-derived mass trend is the least. Compared with SLR-based C\({}_{20}\) in TN11, mass trends derived by SLR-based C\({}_{20}\) in TN14 are 30%-50% more negative (by exceeding 11 Gt/yr) over the AIS. It should be noted that the differences between SLR-based C\({}_{20}\) estimates in TN11 and TN14 are mainly attributed to the different data reduction arc lengths and the application of the GRACE-derived forward model [13]. The differences between \(C_{20}\) estimates in TN07 and TN11 may result from the applied background models corresponding to GRACE RL05 and RL06 data, respectively, e.g., the modeled ocean and atmosphere signal using the Level-1B Atmosphere Ocean De-aliasing product, the mean pole definition and pole tides, and so on [34]. More details about the approaches to solve for SLR-based C\({}_{20}\) estimates can be found in [7; 9; 13].