SUMMARY Gravity Recovery and Climate Experiment (GRACE) Spherical Harmonics (SH) solutions are usually provided together with the corresponding formal errors, however, all multichannel singular spectrum analysis (MSSA) approaches neglect the formal errors of SH coefficients in processing the GRACE time-series. In this contribution, we propose a weighted MSSA to directly process the incomplete time-series of GRACE monthly gravity models by taking the formal errors into account. A 14-yr time-series of Release 06 (RL06) monthly gravity field models from the Center for Space Research (CSR) truncated to degree and order 60 for the period April 2002 to August 2016 is analysed by weighted MSSA, the results are compared with those from the improved MSSA that directly processes the incomplete time-series without considering the formal errors. The first 10 principal components derived by using the weighted MSSA can capture the variance in total up to 82.05 per cent, higher than 80.19 per cent by the improved MSSA. All the fitting errors of GRACE SH coefficients by the weighted MSSA are smaller than those by the improved MSSA, which indicates that weighted MSSA can extract more geophysical signals than the improved MSSA approach. To evaluate the efficiency of the weighted MSSA to eliminate noise, the ratios of the latitude weighted RMS of signals over lands and oceans are computed. Based on all the available months of GRACE solutions, the mean RMS ratio of signals over lands relative to oceans derived by the weighted MSSA is 5.04, higher than 4.96 by the improved MSSA. Therefore, we can conclude that the proposed weighted MSSA can suppress noise more efficiently and extract more geophysical signals from the GRACE time-series, which highlights the necessity of considering formal errors and the effectiveness of the weighted MSSA in post-processing the GRACE monthly gravity field models.

中文翻译：

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考虑形式误差的后处理 GRACE 月度重力场模型的加权多通道奇异谱分析

总结 重力恢复和气候实验 (GRACE) 球谐函数 (SH) 解通常与相应的形式误差一起提供，然而，所有多通道奇异谱分析 (MSSA) 方法在处理 GRACE 时间序列时都忽略了 SH 系数的形式误差. 在这篇文章中，我们提出了一个加权 MSSA，通过考虑形式误差来直接处理 GRACE 月重力模型的不完整时间序列。通过加权 MSSA 分析来自空间研究中心 (CSR) 的 2002 年 4 月至 2016 年 8 月期间截断为 60 度和阶数的 14 年时间序列 Release 06 (RL06) 月度重力场模型，并比较结果与那些来自改进的 MSSA 的那些直接处理不完整的时间序列而不考虑形式错误。使用加权 M​​SSA 导出的前 10 个主成分总共可以捕捉到高达 82.05% 的方差，高于改进的 MSSA 的 80.19%。加权 MSSA 对 GRACE SH 系数的拟合误差均小于改进 MSSA 的拟合误差，表明加权 MSSA 比改进的 MSSA 方法可以提取更多的地球物理信号。为了评估加权 MSSA 消除噪声的效率，计算了陆地和海洋信号的纬度加权 RMS 的比率。根据 GRACE 解决方案的所有可用月份，加权 MSSA 得出的陆地信号与海洋信号的平均 RMS 比为 5.04，高于改进的 MSSA 的 4.96。所以，