Progress and prospect of GRACE Mascon product and its application
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摘要: 2002年重力卫星GRACE的成功发射极大地促进了地球科学多个领域，包括全球海平面变化、极地冰盖与高山冰川消融、水文以及固体地球等多个领域的发展. 然而，GRACE观测数据主要是以球谐系数的形式给出，需要应用者进行一系列预处理才可以得到对应的物理量. 为了克服此困难，也为了提高GRACE恢复重力场地空间分辨率，相关机构在近些年推出了新一代GRACE观测数据产品，即Mascon产品. 该产品的初衷是便于非大地测量和地球物理专业的人使用，比如水文学家、海洋学家，它无需进行任何后处理过程，使用上更加方便. 然而，尽管Mascon产品以较高的空间分辨率（如1°）给出，但是，该产品的应用范围以及其实际的分辨率等都是科学家们非常关注的问题. 目前科学家们已经对该产品在不同流域尺度以及不同应用领域上的适用性问题进行了系统性地评估. 本文综合介绍了Mascon产品的基本原理和方法、三家Mascon产品的差异，并梳理了该产品和球谐系数产品之间在一些具体物理问题的应用中的适用性以及应该注意的问题，为广大科研工作者提供科学依据和使用参考.Abstract: The success of the launch of GRACE in 2002 has greatly promoted the development of Earth Science, especially in many fields such as global sea level change, polar ice sheet and Alpine glacier melting, hydrology and solid earth. However, GRACE observation data are mainly given in the form of spherical harmonic coefficients, so users need to carry out a series of pre-processing to get specific physical quantities. In order to overcome this difficulty and enhance the spatial resolution, relevant organizations have released a new generation of GRACE products, named Mascon products. The original intention of this product is to be convenient for people who are not majoring in Geodesy and Geophysics, such as hydrologists and oceanographers, and it does not need any post-processing process, so it is more convenient to use. Although Mascon product gives a high spatial resolution (such as 1°), scientists are very concerned about the actual resolution and the application scope of the product. At present, scientists have systematically evaluated and applied the applicability of this product in different watershed scales and different application fields. In this paper, we introduce the basic principles and methods of Mascon products, compares the differences between the three Mascon products, and combs the applicability of the products and spherical harmonic coefficient products in the application of some specific physical problems as well as the problems that should be paid attention to, so as to provide scientific basis and use reference for the majority of scientific researchers.
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Key words:
- gravity satellites /
- GRACE /
- Mascon /
- Terrestrial Water Storage (TWS) /
- seismic /
- climate change
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图 1 JPL Mascon产品的格网划分（修改自Watkins et al., 2015）
Figure 1. Definition of JPL Mascon products (modified from Watkins et al., 2015)
图 2 全球TWSA长期趋势的阶振幅，用EWH表示，包括5种产品：CSR Mascon、未经过滤波的球谐系数、经过300 km高斯滤波的球谐系数、加入了尺度因子的格网球谐系数的阶振幅曲线比较. 其中Mascon产品展开到120阶（修改自Zhang L et al., 2019）
Figure 2. Degree amplitudes of global long-term trend TWSA expressed in EWH for five data sets: the CSR Mascon products, spherical harmonic solutions without any filter, spherical harmonic solutions applying a Gaussian filter with radius of 300km, spherical harmonic solutions applying a DDK4 filter, Gridded spherical harmonic solutions (modified from Zhang L et al., 2019)
图 3 JPL Mascon产品对陆地信号泄露到海洋的处理（Watkins et al., 2015）. 色彩标尺为2011年4月质量异常，用等效水高表示
Figure 3. The correcting for leakage errors due to mascon placement over land/ocean boundaries of JPL Mascon products (Watkins et al., 2015). The color bar refers to the mass anomalies for April 2011 of EWH
图 4 CSR Mascon求解过程中，正则化球谐系数计算的全球RMS值泄露误差改正. （a）正则化球谐系数计算的全球RMS值；（b）为了避免泄露误差，经过重新调整后的全球RMS值（Save et al., 2016）
Figure 4. Correction of the leakage of the global RMS grid of the variability of the regularized spherical harmonic solutions. (a) Global RMS grid of the variability of the regularized spherical harmonic solutions; (b) Readjustment global RMS from Fig. (a) (Save et al., 2016)
图 5 GRACE产品在南美洲陆地水储量长期趋势的比较. （a）CSR Mascon；（b）Tellus官网格网球谐系数产品（加入了尺度因子）；（c）JPL Mascon（修改自Save et al., 2016）
Figure 5. Comparison of the long-term trend of the TWS among GRACE products in South America. (a) CSR Mascon; (b) Tellus land Grids from the official website (added the scale factors); (c) JPL Mascon (modified from Save et al., 2016)
图 6 （a）南极、格林兰岛冰盖与阿拉斯加湾冰川的GSFC Mascon块设置；（b）利用这种Mascon设置估算的格林兰岛冰盖2004～2010年年均质量平衡（修改自Luthcke et al., 2013）
Figure 6. (a) The defined of the GSFC Mascon of the Antarctic and Greenland ice sheets and Gulf of Alaska glaciers. (b) The mean annual mass balances of the Greenland ice sheets during 2004～2010 (modified from Luthcke et al., 2013)
图 7 Jacob等（2012）对全球冰川覆盖地区的Mascon块设置
Figure 7. Mascons for the ice-covered regions considered by Jacob et al. (2012)
图 8 Yang等（2020）利用Mascon产品评估不同水文模型在澳大利亚流域的准确性. 其中子图（a）～（g）为不同水文模型；（h）是JPL、CSR、GSFC Mascon结果的平均
Figure 8. Yang et al. (2020) using the Mascon products to evaluate the accuracy of different water models in Australian basin. (a)~(g) are water models, (h) is the average of the results of JPL, CSR, and GSFC Mascon
图 9 利用直接法、反演法和JPL Mascon估计的全球海平面变化（修改自 Uebbing et al., 2019）
Figure 9. The global sea level change estimated by direct, inversion methods and JPL Mascon (modified from Uebbing et al., 2019)
图 10 CSR、JPL Mascon和球谐系数产品在面积大小不同的176个流域的陆地水储量估计不确定性（修改自Scanlon et al., 2016）
Figure 10. The uncertainty of the TWSA of the 176 basins with different area observed from CSR、JPL Mascon and spherical harmonic products (modified from Scanlon et al., 2016)
图 11 CSR Mascon、球谐系数经过DDK4滤波以及加入了尺度因子的格网球谐系数产品在龙羊峡水库的月重力场恢复. 可以看到在反映龙羊峡水位抬升事件上，Mascon表现并没有其余两个球谐系数产品结果好（修改自Zhang L et al., 2019）
Figure 11. The monthly gravity field of Longyangxia reservoir is restored by CSR mascon, spherical harmonic coefficient filtered by DDK4 and grid spherical harmonic coefficient product with scale factor. It can be seen that mascon's performance is not as good as the other two spherical harmonic coefficient products in reflecting the water level rise event of Longyangxia reservoir (modified from Zhang L et al., 2019)
图 12 GRACE恢复的东日本大地震同震重力信号. （a）CSR Mascon产品的同震重力信号；（b）图（a）经过300 km高斯滤波；（c）CSR球谐系数产品的同震重力信号（Zhang et al., 2020）
Figure 12. The coseismic gravity signal of the great east Japan earthquake recovered by grace. (a) Coseismic gravity signal of CSR mascon products; (b) Fig. (a) is filtered by 300 km Gaussian filter; (c) Coseismic gravity signals of CSR products with spherical harmonic coefficients ( Zhang et al., 2020)
图 13 GRACE恢复的三个较小地震的同震重力变化. （a）2013年5月24日鄂霍次克海深海地震（MW8.3）;（b）2007年9月12日明古鲁地震（MW8.5）；（c）2012年4月11日苏门答腊/印度洋双震（MW8.6+MW8.2）. 左列为Mascon产品，右列为球谐系数产品（SH），并做300 km的高斯滤波和去相关滤波，单位为µGal（修改自Zhang et al., 2020）
Figure 13. Co-seismic gravity changes derived from GRACE data. (a) the 2013 Okahotsk event (MW8.3); (b) 2007 Benkulu event (MW8.5); (c) 2012 Sumatra/Indian Ocean event (MW8.6+MW8.2). The left column is Mascon product, and the right column is spherical harmonic product and applying a Gassian filter with radius of 300 km and a P4M6 filter, the unit is µGal (modified from Zhang et al., 2020)
表 1 三家官方机构最新版本的Mascon产品参数对比
Table 1. The parameters of the latest Mascon products of three official organizations
JPL CSR GSFC 格网大小 0.5°×0.5° 0.25°×0.25° 1°×1° 时间采样 1个月 1个月 10天 格网形状 圆盘形 正六边形 正方形 原始分辨率 3°×3° 1°×1° 1°×1° 总格网数 4551 41000 41168 基于数据 L1b级星间距和GPS数据 L2级球谐系数数据 L1b级星间距和GPS数据 有无外部物理模型
先验约束有 无 有 关键技术 基于先验信息的白噪声建模；
连续卡尔曼滤波Tikhonov正则化方法；
L曲线法迭代求解；
自协方差矩阵的正则化
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