## 1 Introduction  
With its launch in March 2002, the Gravity Recovery and Climate Experiment (GRACE) mission provided unique observations about the Earth's temporal gravity field with unprecedented accuracy [1]. Its data record covered more than 15 years, largely improving our understanding of terrestrial water storage change, ice sheet mass balance, and glacier mass variations, as well as sea level change [2]. GRACE-based temporal gravity field solutions in the standard Level 2 (L2) data product consist of a series of spherical harmonic coefficients with degree and order up to at least 60. Due in part to the geometry of satellite constellation, it was stated early in the mission that the GRACE-determined degree-2 zonal term, \(C_{20}\), was not reliable [3; 4]. Previous studies reported that an unexpected \(\sim\)161-day periodic signal was contained in GRACE-determined \(C_{20}\) values, with the cause attributed to aliasing of the S2 ocean tide [5; 6]. It is worth noting that this is not a consensus view. The authors of [7] suggested a cause associated with the temperature-dependent systematic error in the accelerometer data. Regardless of the true cause, it has become a standard procedure to replace GRACE-determined \(C_{20}\) values with those provided by satellite laser ranging (SLR) data in order to accurately derive mass redistribution within the Earth's system using GRACE monthly gravity field solutions. Indeed, SLR observations to geodetic satellites include valuable information about the low degree/order components of the Earth gravity field [8; 9]. SLR can accurately measure the long-term variations in \(C_{20}\), which provides an independent constraint on GRACE-determined \(C_{20}\)[10]. Previously, the estimates of \(C_{20}\) from SLR were documented in GRACE Technical Note (TN), together with a version number. For instance, TN07 for GRACE L2 Release 05 (RL05) data [11] and TN11 for GRACE Release 06 (RL06) data [7]. However, as the authors of [7] mentioned, there was a concern that SLR-provided \(C_{20}\) values could be inconsistent with the other spherical harmonic coefficients in GRACE monthly solutions. They compared \(C_{20}\) estimates from SLR only and from the combination of SLR and GRACE, with the results concluding that estimates of \(C_{20}\) from SLR only were appropriate for science applications of GRACE data. This did not dispel the concern that the SLR \(C_{20}\) estimates could not be used to stand in for GRACE [12]. The authors of [13] recommended a new \(C_{20}\) product which was obtained by including GRACE-derived time-variable gravity in the SLR data reduction forward modeling. This new \(C_{20}\) product was produced at the Goddard Space Flight Center (GSFC) and documented in TN14 for GRACE RL06 and GRACE-Follow-On (GRACE-FO) data. Besides, estimates of SLR-based \(C_{30}\) (GSFC \(C_{30}\)) since March 2012 are also provided in TN14, aiming at improving the accuracy of GRACE-derived mass redistribution during the degradation of GRACE \(C_{30}\) for single accelerometer mode [14]. However, some recent studies adopted the GSFC \(C_{30}\) product in TN14 since March 2012 instead of GRACE-determined \(C_{30}\)[15; 16]. In addition, the authors [17] published SLR-based \(C_{20}\) solutions specifically for GRACE RL06 data published by Deutsches GeoForschungsZentrum (GFZ), German Research Centre for Geosciences. Apparently, different low degree zonal harmonic coefficients may cause discrepancies among GRACE-derived mass redistribution. It was recognized that these low degree zonal harmonics derived from SLR have non-negligible impacts on accurately deriving mass redistribution from GRACE data [15; 18]. Accurately deriving mass redistribution from GRACE data also necessitates the inclusion of geocenter motion, which depends only on the degree one coefficients of surface load [19; 20; 21; 22].