Abstract The error variance-covariance matrices of the monthly GRACE gravity field models are usually well-structured (e.g., order-leading) to contain the error information of the monthly gravity field models, and they are important information to further improve the accuracy of the estimated mass transportation by a post-processing scheme. Intensive studies have been performed to understand the impact of different approximations of the full error variance-covariance matrix on the mass estimates obtained with the conventional GRACE-post processing methods (e.g., the de-striping method). In this study, based on the variants of the mascon approach which treat monthly GRACE solutions as input, we consider four different structures to the error variance-covariance matrix, (i) full matrix, (ii) block diagonal matrix, (iii) diagonal matrix, and (iv) identity matrix, and examine their impact on the mass transport estimates in Greenland. Using both synthetic and real data, we analyze the results at four temporal scales: (i) the long-term decadal scale, (ii) the inter-annual scale, (iii) the seasonal scale, and (iv) the monthly scale. Based on the synthetic study, we find that for the recovery of the long-term trend, the application of the diagonal structure obtains the best estimates. This is caused by the amplification of the model error in the mascon approach when considering the full and block diagonal structures of error variance-covariance matrix, not due to any imperfection of them. Therefore, we emphasize that one should be aware of mascon model deficiency in the mascon approach. Furthermore, the best inter-annual, seasonal and monthly mass estimates are derived by considering the block diagonal and full structures. This is caused by the behavior of the bias and the unique parameterization error in the case of different structures. A similar finding is also presented in the real data case. Finally, our analysis denotes the necessity of releasing the block diagonal structure together with the official monthly gravity field model for the GRACE Follow-On mission, instead of releasing only the diagonal structure as done for the GRACE mission.

中文翻译：

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GRACE重力解误差协方差矩阵结构对格陵兰冰盖质量通量估计的影响

摘要 月度GRACE重力场模型的误差方差-协方差矩阵通常结构良好（如阶次领先）以包含月度重力场模型的误差信息，是进一步提高重力场模型精度的重要信息。通过后处理方案估计的大众运输。已经进行了深入研究以了解完整误差方差-协方差矩阵的不同近似值对使用传统 GRACE 后处理方法（例如，去条带化方法）获得的质量估计值的影响。在本研究中，基于将月度 GRACE 解作为输入的 mascon 方法的变体，我们考虑了误差方差-协方差矩阵的四种不同结构，（i）完整矩阵，（ii）块对角矩阵，（iii）对角矩阵矩阵，(iv) 单位矩阵，并检查它们对格陵兰公共交通估计的影响。使用合成数据和真实数据，我们分析了四个时间尺度的结果：(i) 长期十年尺度，(ii) 年际尺度，(iii) 季节尺度，以及 (iv) 月尺度。在综合研究的基础上，我们发现对于长期趋势的恢复，对角结构的应用获得了最好的估计。这是由于在考虑误差方差-协方差矩阵的全对角线结构和块对角线结构时，mascon 方法中模型误差的放大引起的，而不是由于它们的任何缺陷。因此，我们强调在 mascon 方法中应该意识到 mascon 模型的缺陷。此外，最好的跨年，通过考虑块对角线和完整结构得出季节性和每月质量估计值。这是由偏差的行为和不同结构情况下的独特参数化错误引起的。类似的发现也出现在真实的数据案例中。最后，我们的分析表明有必要在 GRACE Follow-On 任务中与官方月度重力场模型一起发布块对角结构，而不是像 GRACE 任务那样只发布对角结构。