# Separation and Recovery of Geophysical Signals Based on the Kalman Filter with GRACE Gravity Data

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. The Kalman Filter Approach

#### 2.2. Prior Information

#### 2.3. Multiple Gridded-Gain Factors

## 3. Results

_{2,0}terms with results observed by satellite laser ranging [37], and the Degree-1 terms obtained by the method of Swenson et al. [38] in the form of Stokes coefficients. The updated time series for these terms can be downloaded from PODAAC. Lastly, the results of the Kalman filter expressed as EWH Were compared with the traditional filtering results (P3M6+Fan filter, smoothing radius of 300 km) and the mascon products released by CSR. After separating geophysical signals from GRACE Level-2 data, we needed to correct the truncation error. Therefore, we first used simulation data to test the performance of multiple gridded-gain factors proposed in this article.

#### 3.1. The Performance of Multiple Gridded-Gain Factors

#### 3.2. Monthly Variations of the Separated Signal and Stripe Noise

#### 3.3. Comparison with a Commonly Used Filter

^{2}(the Orinoco River Basin) to ∼2,160,000 km

^{2}(Greenland). Figure 9a–f are ordered by increasing area.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The components of the geophysical signal part in the synthetic model including (

**a**) GLDAS, (

**b**) OBP, (

**c**) GRACE (unfiltered) expressed as the equivalent water height (EWH, unit: cm), and (

**d**) GIA expressed as the EWH rate (unit: mm/year).

**Figure 2.**Prior covariance matrices used in the Kalman filter: (

**a**) covariance matrix of geophysical signal, (

**b**) the covariance matrix of stripe noise, and (

**c**) the Gaussian white noise covariance matrix (with dimension 3717 × 3717, provided by CSR) of the observation, expressed in logarithmic scale (log

_{10}).

**Figure 3.**Time series of surface mass variations at two grid points: (

**a**) located at (75.5°W, 12.5S) and (

**b**) located at (76.5°W, 10.5S). These time series include the variations derived from the original synthetic model (red), the truncated result (black), signals restored by single gridded-gain factors (blue), and signals restored by multiple gridded-gain factors (green) at both grid points.

**Figure 4.**Monthly surface mass variations (from June 2002 to December 2002) separated from the Kalman filter, using GRACE RL05 Level-2 monthly gravity solutions. The estimates have been recovered by multiple gridded-gain factors.

**Figure 5.**Monthly stripe error variations (from June 2002 to December 2002) separated from the Kalman filter, using GRACE RL05 Level-2 monthly gravity solutions.

**Figure 6.**GRACE-derived maps of surface mass variations. The left column is filtered with the P3M6 and smoothed with 300 km Fan, and the right column applies the Kalman filter.

**Figure 7.**Comparison of the reduction ratio of the WRMS values derived from the results of the Kalman filter (left) and the commonly used filtering method (right).

**Figure 8.**The estimates of secular trend (left column) and annual amplitude (right column) applying P3M6 and Fan (300 km) filter (the top row), the Kalman filter (the middle row), and the mascon method (the bottom row).

**Figure 9.**Comparison of the average mass variations over different basins estimated by the commonly used filter (in red), the Kalman filter (in green), and the mascon solution (in blue). The plots from (

**a**–

**f**) are ordered by increasing area, and their scales are different.

**Table 1.**The root mean square (RMS) of the surface mass variation differences between the original synthetic model and the data derived from different approaches in different regions (unit in mm).

Point/Region | RMS1 ^{1} | RMS2 ^{2} | RMS3 ^{3} |
---|---|---|---|

Point of Figure 3a | 30.32 | 26.82 | 7.77 |

Point of Figure 3b | 34.19 | 31.18 | 9.74 |

Amazon | 7.24 | 6.35 | 4.46 |

Mississippi | 4.31 | 3.68 | 2.31 |

Yangtze River | 4.82 | 4.39 | 2.93 |

Greenland | 40.60 | 10.94 | 7.31 |

Antarctica | 12.24 | 6.87 | 4.22 |

^{1}The RMS of the surface mass variation difference obtained by the original synthetic model and the truncated result.

^{2}The RMS of the surface mass variation difference obtained by the original synthetic model and the single factor.

^{3}The RMS of the surface mass variation difference obtained by the original synthetic model and multiple gridded-gain factors.

**Table 2.**Statistics of the WRMS reduction ratio derived from the results of the Kalman filter and the commonly used filtering method.

Method | Max | Min | Median | Number (>0) |
---|---|---|---|---|

Kalman filter | 0.788 | −0.303 | 0.302 | 162 |

P3M6 and Fan filter | 0.769 | −0.312 | 0.266 | 159 |

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**MDPI and ACS Style**

Wang, X.; Luo, Z.; Zhong, B.; Wu, Y.; Huang, Z.; Zhou, H.; Li, Q.
Separation and Recovery of Geophysical Signals Based on the Kalman Filter with GRACE Gravity Data. *Remote Sens.* **2019**, *11*, 393.
https://doi.org/10.3390/rs11040393

**AMA Style**

Wang X, Luo Z, Zhong B, Wu Y, Huang Z, Zhou H, Li Q.
Separation and Recovery of Geophysical Signals Based on the Kalman Filter with GRACE Gravity Data. *Remote Sensing*. 2019; 11(4):393.
https://doi.org/10.3390/rs11040393

**Chicago/Turabian Style**

Wang, Xiaolong, Zhicai Luo, Bo Zhong, Yihao Wu, Zhengkai Huang, Hao Zhou, and Qiong Li.
2019. "Separation and Recovery of Geophysical Signals Based on the Kalman Filter with GRACE Gravity Data" *Remote Sensing* 11, no. 4: 393.
https://doi.org/10.3390/rs11040393