A new approach to recover time-variable gravity fields from satellite laser ranging (SLR) is presented. It takes up the concept of lumped coefficients by representing the temporal changes of the Earth’s gravity field by spatial patterns via combinations of spherical harmonics. These patterns are derived from the GRACE mission by decomposing the series of monthly gravity field solutions into empirical orthogonal functions (EOFs). The basic idea of the approach is then to use the leading EOFs as base functions in the gravity field modelling and to adjust the respective scaling factors straightforward within the dynamic orbit computation; only for the lowest degrees, the spherical harmonic coefficients are estimated separately. As a result, the estimated gravity fields have formally the same spatial resolution as GRACE. It is shown that, within the GRACE time frame, both the secular and the seasonal signals in the GRACE time series are reproduced with high accuracy. In the period prior to GRACE, the SLR solutions are in good agreement with other techniques and models and confirm, for instance, that the Greenland ice sheet was stable until the late 1990s. Further validation is done with the first monthly fields from GRACE Follow-On, showing a similar agreement as with GRACE itself. Significant differences to the reference data only emerge occasionally when zooming into smaller river basins with strong interannual mass variations. In such cases, the approach reaches its limits which are set by the low spectral sensitivity of the SLR satellites and the strong constraints exerted by the EOFs. The benefit achieved by the enhanced spatial resolution has to be seen, therefore, primarily in the proper capturing of the mass signal in medium or large areas rather than in the opportunity to focus on isolated spatial details.

中文翻译：

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从卫星激光测距中恢复高分辨率时间重力场的混合方法

提出了一种从卫星激光测距 (SLR) 中恢复时变重力场的新方法。它采用了集总系数的概念，通过球谐函数的组合以空间模式表示地球重力场的时间变化。这些模式源自 GRACE 任务，通过将一系列月重力场解分解为经验正交函数 (EOF)。该方法的基本思想是在重力场建模中使用领先的 EOF 作为基函数，并在动态轨道计算中直接调整相应的比例因子；仅针对最低度数，单独估计球谐系数。因此，估计的重力场在形式上与 GRACE 具有相同的空间分辨率。结果表明，在 GRACE 时间范围内，GRACE 时间序列中的长期和季节性信号均以高精度再现。在 GRACE 之前的时期，SLR 解与其他技术和模型非常吻合，并证实格陵兰冰盖在 1990 年代后期之前是稳定的。对 GRACE Follow-On 的第一个月度字段进行了进一步验证，显示出与 GRACE 本身类似的协议。当放大到具有强烈年际质量变化的较小流域时，与参考数据的显着差异只是偶尔出现。在这种情况下，该方法达到了由 SLR 卫星的低光谱灵敏度和 EOF 施加的强约束所设定的极限。因此，必须看到增强空间分辨率所带来的好处，