GRACE数据后处理方法--迭代恢复方法

【背景】对于地球重力场的应用问题，我们需求高时空分辨率和信噪比，而GRACE较低的空间分辨率成为限制其发展的一个重要因素。由万有引力定律可知，引力随着距离的平方衰减。这种衰减还依赖于波长，即随着距离的增加，短波引力异常比长波场衰减得更为迅速（The National Council, 1997）。轨道高度上的卫星观测得到的信号相比于地表的重力信号，其经过衰减并且含有各类误差和噪声。为了恢复真实的地表重力信号，我们需要把卫星观测信号向下延拓，一般乘上衰减因子的倒数进行信号放大，以得到地表真实的重力信号。但是如此一来也放大了观测误差，导致高阶信号被污染。因此需要对GRACE球谐产品进行后续的反演恢复。

Chen et al.(2013)在nature geoscience中发表文章《Contribution of ice sheet and mountain glacier melt to recent sea level rise》，文章内容如下：

The global forward modelling can more effectively reduce the leakage effect between terrestrial and ocean signals, and help reconstruct true mass rates of the ocean, polar ice sheets, mountain glaciers and TWS at the same time. Full details of the forward modelling approach are provided in the Supplementary Information. A brief synopsis is as follows: on a global 1◦ ×1 ◦ grid, we first assign initial trial mass rates (for example, GRACE apparent mass rates after filtering and smoothing) to each grid point over land, and a uniform layer of water is added to the oceans to conserve total mass. The trial mass rate grid is converted into spherical harmonics (with the same resolution as GRACE data); we then convert the spherical harmonics of the trial mass rate grid back to a spatial grid after applying GRACE data processing procedures to the spherical harmonic representation of the trial mass field (including truncation and smoothing); we compare the processed trial spatial grid with the GRACE apparent mass rate grid and adjust the trial mass rates accordingly. These three steps are repeated iteratively, until the processed trial mass rate grid matches the GRACE apparent mass rate grid. This provides a single mass rate estimate for the oceans, which conserves mass globally, because terrestrial rates are estimated simultaneously. Averages for specific regions (such as Antarctica) can also be calculated.

简单而言，该方法的原理是在迭代拟合的每一步中，观察信号和模型信号之间的差值，并在下一步中加入模型中。步骤如下：

（1）平滑后的1度分辨率的等效水高作为输入模型；

（2）将输入模型球谐展开，采用与GRACE一样的滤波处理方法，得到恢复信号；

（3）计算恢复信号与原始信号的差值，并回加到原始输入模型；

（4）重复第2、3步，直至收敛。

下面我们展示利用迭代法恢复的信号对比。我们可以看到，经过迭代之后的信号振幅得到恢复，而经过球谐展开和滤波得到的结果与原结果类似。

参考文献

Chen, J., Wilson, C. & Tapley, B. Contribution of ice sheet and mountain glacier melt to recent sea level rise. Nature Geosci 6, 549–552 (2013). https://doi.org/10.1038/ngeo1829