反演地表质量变化的附有方差约束的径向点质量方法

针对目前径向点质量方法在反演GRACE (Gravity Recovery and Climate Experiment)时变地球重力场信号时条带噪声和泄漏误差较大的问题，本文提出了一种附有方差约束的径向点质量方法(Variance Constrained Radial Point-Mass Method，VCPM).该方法利用质量块的先验方差信息设计正则化矩阵对质量变化反演进行空间约束，同时为了解决单一的正则化参数不能适应全球质量变化大小不均匀的问题，构建了迭代的正则化处理策略.为了检验VCPM方法的可靠性，本文反演了2003-01-2014-11全球地表质量变化，并与GRACE球谐位系数法、GLDAS2.1水文模型、CSR (University of Texas Center for Space Research，德克萨斯大学空间研究中心)与JPL (Jet Propulsion Laboratory，喷气推进实验室) RL06 Mascon数据在全球的均方根误差、长期趋势、周年振幅以及局部的冰冻圈、陆地流域质量变化进行了对比分析.结果显示VCPM与CSR Mascon在全球、陆地和海洋区域的RMSE按面积加权平均值分别为2.12 cm、4.16 cm和1.
25 cm，在全球和陆地区域均低于CSR Mascon与JPL Mascon的相应RMSE (2.22 cm和4.62 cm)，在海洋区域仅略大于CSR Mascon与JPL Mascon的RMSE (1.18 cm)；在8个陆地流域和内陆海域的时间序列对比中，VCPM与两种Mascon数据在扣除季节项和趋势项后的相关系数在绝大多数区域仍能达到0.86以上；另外相对于传统点质量方法和球谐位系数法，VCPM能有效抑制南极和格陵兰岛等区域的泄漏误差.这表明本文所提出的VCPM方法可以有效去除条带误差、抑制海陆信号泄漏且大幅提高反演结果的精度和空间分辨率，从而为计算高精度高分辨率地表质量变化提供了一种可供选择的有效途径.

Variance constraint radial point-mass method for inversion of earth surface mass variation

In order to overcome the problem of large stripes error and leakage error when using radial point mass method for inversion of GRACE time-varying gravity field, a variance constraint radial point mass method (VCPM) is developed in this study. In this method, the prior variance information of mass blocks is used to design regularization matrix and provides constrain for the inversion procedure. Besides, the iterative regularization method is applied to solve the problem that a single regularization parameter cannot adapt to the uneven global mass variation. In order to validate the reliability of the promoted method, the global mass variation from January 2003 to November 2014 are calculated, and then are compared with results from the GRACE spherical harmonic method, GLDAS2.1 hydrological model, CSR/JPL RL06 Mascon in terms of global root mean square error (RMSE), long-term trend, annual amplitude, local cryosphere and land basins. The result shows that the values of RMSE of differences between VCPM and CSR Mascon over global, continental and ocean areas are 2.12 cm, 4.16 cm and 1.
25 cm respectively, which are lower than that of JPL Mascon and CSR Mascon (2.22 cm and 4.62 cm) in global and terrestrial areas, and slightly higher than that of CSR Mascon and JPL Mascon (1.18 cm) in ocean areas. The time series over 8 land basins and inland sea areas are calculated based on the VCPM and two kinds of Mascon datasets, the correlation coefficients between these results would be larger than 0.86 in most regions. In addition, compared with the traditional point mass method and spherical harmonic potential coefficients method, the VCPM can effectively suppress leakage errors in areas such as Antarctica and Greenland, which indicates that the VCPM method developed in this study could effectively constrain the stripes error, decrease the sea-land signal leakage and greatly improve the accuracy and spatial resolution of the estimated results. Therefore, the VCPM would provide an effective method for calculating earth's surface mass variation with high precision and resolution.