利用径向基函数RBF解算GRACE全球时变重力场

本文利用GRACE（Gravity Recovery And Climate Experiment）level 1b数据和径向基函数RBF（radial basis function）方法解算了全球时变地球重力场.RBF基函数相比传统球谐（spherical harmonic）基函数，其高度的空域局部特性使得正则化过程易于添加先验协方差信息，从而可能揭示更加准确的重力场信号.本文研究表明，RBF基函数算法在精化现有的GRACE全球时变重力场模型，如提升部分区域信号幅度等方面具有一定优势.本文通过将RBF的尺度因子作为待解参数，基于GRACE卫星的Level 1b数据和变分方程法，成功获取了2009-2010年90阶无约束全球时变重力场RBF模型Hust-IGG03，以及正则化全球时变重力场RBF模型Hust-IGG04.通过与GRACE官方数据处理中心GFZ发布的最新90阶球谐基时变模型RL05a进行对比，结果表明：（1）无约束RBF模型Hust-IGG03和GFZ RL05a在空域和频域表现基本一致；（2）正则化RBF模型Hust-IGG04无需进行后处理滤波已经显示较高信噪比，噪音水平接近于球谐基模型GFZ RL05a经400 km高斯滤波后的效果；（3）Hust-IGG04相比400 km高斯滤波GFZ RL05a在周年振幅图和趋势图上显示出更多的细节信息，并且呈现出更强的信号幅度，如在格陵兰冰川融化趋势估计上Hust-IGG04比GFZ RL05a提高了24.2%.以上结果均显示RBF方法有助于进一步挖掘GRACE观测值所包含的时变重力场信息.

GRACE global temporal gravity recovery through the radial basis function approach

Unlike the classical SH (spherical harmonic) geopotential representation employed by most of GRACE data processing centers to recover temporal gravity fields, this study manages to retrieve temporal gravity signal by the regional geopotential representation RBF (radial basis function), which features to be highly spatially localized. RBF is known as a more appropriate base than the spherical harmonics, since it is easy to incorporate with regional geophysical a-priori information in regularization to model detailed gravity field accurately. As a trial of RBF implementation in global gravity recovery from GRACE observations, this study assumes RBF scaling factors rather than Stokes coefficients as the unknowns within the gravity inversion. In this way, we successfully generated the RBF-based unconstrained model (namely, Hust-IGG03) as well as its constrained version (namely, Hust-IGG04). By making comparisons among GFZ RL05a, Hust-IGG03 and Hust-IGG04 over 2009-2010, we found that: (1) the degree geoid heights as well as the spatial equivalent water heights of Hust-IGG03 agree with those of GFZ RL05a in each month, revealing that unconstrained RBF solution is comparable to SH solution without the concern of signal loss; (2) with an unit Tikhonov regularization matrix applied, Hust-IGG04 has evidently eliminated the striping error that can severely bias the true gravity signal, and Hust-IGG04 has a similar noise level as GFZ RL05a after Gauss filtering with radius of 400km. Therefore users don't necessarily carry out the post-processing filtering on Hust-IGG04 to suppress noise any more; (3) Hust-IGG04 retrieved the gravity signal in a higher resolution than the filtered GFZ RL05a product, on both of annual amplitude map and trend map during the period of 2009-2010, for instance Hust-IGG04 increased the ice-melting rate over southern Greenland by 24% with respect to the filtered GFZ RL05a product. Consequently, we suggest that RBF is not only able to detect comparable gravity signals as the classical SH method, but also achieve a higher signal resolution due to its feasibility of introducing a-priori information into regularization. We anticipate that RBF can better exploit current or future GRACE observations and thereby contributes to the refinement of the regional gravity modelling for China.