﻿ 基于经验正交函数分解的GRACE时变地球重力场滤波处理
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 大地测量与地球动力学  2019, Vol. 39 Issue (4): 366-370  DOI: 10.14075/j.jgg.2019.04.007

### 引用本文

WANG Chenyan, YOU Wei, FAN Dongming. GRACE Time-Variable Gravity Field Filtering Based on Empirical Orthogonal Function Decomposition[J]. Journal of Geodesy and Geodynamics, 2019, 39(4): 366-370.

### Foundation support

National Natural Science Foundation of China, No.41574018, 41604068, 41440018.

### Corresponding author

YOU Wei, PhD, associate professor, majors in satellite gravity measurements and measurement data processing, E-mail:youwei1985@foxmail.com.

### About the first author

WANG Chenyan, postgraduate, majors in GRACE time-varying gravity field and its application, E-mail:1163518721@qq.com.

### 文章历史

1. 西南交通大学地球科学与环境工程学院，成都市高新区西部园区，611756

1 基本原理 1.1 等效水高计算

 $\begin{array}{l} \Delta H\left( {\theta , \lambda } \right) = \frac{{a{\rho _{{\rm{ave}}}}}}{{3{\rho _w}}}\mathop \sum \limits_{l = 0}^\infty \mathop \sum \limits_{m = 0}^l {{\bar P}_{lm}}\left( {\cos \theta } \right){W_l}\frac{{2l + 1}}{{1 + {k_l}}} \times \\ \;\;\;\;\;\;\;\;\;(\Delta {{\bar C}_{lm}}\cos \left( {m\lambda } \right) + \Delta {{\bar S}_{lm}}\sin \left( {m\lambda } \right)) \end{array}$ (1)

1.2 经验正交函数分析方法

 $\mathit{\boldsymbol{X}} = \mathit{\boldsymbol{P}}{\mathit{\boldsymbol{E}}^{\rm{T}}}$ (2)

 $\mathit{\boldsymbol{X}} \cong {\mathit{\boldsymbol{X}}_j} = {\mathit{\boldsymbol{P}}_j}\mathit{\boldsymbol{E}}_j^{\rm{T}}, j < \min \left( {n, p} \right)$ (3)

2 基于经验正交函数的GRACE滤波方法及其改进

 图 1 2008-03不同滤波方法的等效水高 Fig. 1 Equivalent water heights of different filtering methods in March, 2008

3 结果对比分析

 图 2 几种方法计算得到的误差全球分布 Fig. 2 Global distribution of errors calculated by several methods

 图 3 高斯滤波与其他滤波方法的差值 Fig. 3 The difference between the results calculated by Gaussian filtering and other filtering methods

 图 4 由NOAH数据计算得到的2008-03等效水高模拟值 Fig. 4 Simulated equivalent water height calculated from NOAH data in March, 2008

 图 5 3种滤波方法的等效水高及其与等效水高模拟值的差值 Fig. 5 The equivalent water heights of the three filtering methods and their difference from the simulated equivalent water height

4 结语

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GRACE Time-Variable Gravity Field Filtering Based on Empirical Orthogonal Function Decomposition
WANG Chenyan1     YOU Wei1     FAN Dongming1
1. Faculty of Geoscience and Environmental Engineering, Southwest Jiaotong University, Western High-Tec Zone, Chengdu 611756, China
Abstract: In using the GRACE filtering process, the traditional de-correlation filtering method presents difficulties in perfectly preserving the real signal and weakening the stripe error at the same time. In order to solve this problem, the paper makes a certain improvement on the filtering method and combined EOF filtering method with de-correlation filtering method. Several experiments are used to filter real GRACE data and simulated data, respectively. The results show that the improved filtering method inherits the advantages of the EOF filtering method and the de-correlation filtering method. The method weakens the influence of the north-south stripe error as much as possible, while preserving the most realistic signal.
Key words: GRACE; filtering method; empirical orthogonal function; Kolmogorov-Smirnov test