# The Crustal Vertical Deformation Driven by Terrestrial Water Load from 2010 to 2014 in Shaanxi–Gansu–Ningxia Region Based on GRACE and GNSS

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## Abstract

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## 1. Introduction

## 2. Data and Method

#### 2.1. GRACE Data and Postprocessing

_{3}M

_{15}decorrelation filtering. Here, the embedding dimension was 5, and the fitting order was 3. The coefficients of degree 1 were replaced by Sweason’s results [26]. In addition, we modified the expressions of GRACE C

_{20}values by replacing the C

_{20}values from the CSR/GFZ/JPL-RL06 GSM files with the corresponding values from TN11. The TN11 values of SLR-derived C

_{20}are not interchangeable with the TN07 or TN05 values, due to differences in background models and the absence of background rates in the former. For any month without data, the coefficients were derived by averaging values from two adjacent months.

#### 2.2. GNSS Data

#### 2.3. Method

## 3. Result and Analysis

#### 3.1. Leakage Error Correction with Single Scale Factor

#### 3.2. Spatiotemporal Analysis of Vertical Deformation from Terrestrial Water Load

#### 3.3. The Comparison of the Vertical Deformation from GRACE and GNSS

## 4. Discussion

## 5. Conclusions

- (1)
- The comparison results of three hydrological models showed that the correlation coefficient and NSE index of GLDAS model filtering results and GRACE filtering time series were closest to 1, indicating that the scale factor based on the results before and after filtering for GLDAS could effectively restore the GRACE leakage signal, and the scale factor k = 1.21 was calculated.
- (2)
- The surface vertical deformation caused by terrestrial water load in the SGN region from GRACE showed obvious stepladder spatial distribution, and the deformation variables gradually decreased from south to north. The linear rate of surface vertical deformation in the southwest was −0.6 mm/a, while the linear rate in the north and northeast was less, with −0.2 mm/a.
- (3)
- Compared with GNSS, the correlation coefficient and contribution rate of GRACE and GNSS changed significantly before and after GAC correction was applied to GRACE. This indicated that GAC correction is helpful to enhance the consistency between GRACE and GNSS. In addition, both of the annual variation trends were also relatively consistent, but the total mass amplitudes of GRACE and GAC were smaller than those of GNSS. The research results can help to explore the motion mechanism between water migration and surface deformation, which is of benefit in the protection of water’s ecological environment in the region.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**The crustal vertical deformation in SGN region driven by terrestrial water load represented by GRACE and three hydrological models from 2010 to 2014.

**Figure 3.**Linear rate every year for vertical deformation from terrestrial water load in SGN from 2010 to 2014.

**Figure 4.**Vertical deformation series and decomposition signals of terrestrial water load in SGN from 2010 to 2014.

**Figure 5.**The monthly and seasonal vertical deformation maps driven by changes in terrestrial water load.

**Figure 6.**The crustal vertical displacement comparison with 8 CORS data and GRACE before and after GAC correction in SGN from 2010 to 2014.

**Figure 7.**Residual sequences obtained by subtracting GRACE results before and after GAC correction from GNSS vertical displacement sequence.

**Figure 8.**Comparison of GRACE and GAC total mass term time series with vertical time series from 8 CORS in SGN.

Parameter | Processing Mode |
---|---|

Ionosphere delay model | LC_AUTCLN |

Tropospheric model | Saastamoinen + GPT2w + estimation |

Ambiguity resolution | LAMBDA method |

Framework of prior coordinates | ITRF2014 |

Sampling interval data | 15 s |

Satellite cut-off elevation angle (°) | 10 |

Solid tide model | IERS2010 |

Ocean tide model | FES2004(otl_FES2004.grid) |

Inertial framework | J2000 |

Atmospheric mapping function | VMF1 |

Solar radiation pressure model | ECOMC model |

PCO/PCV | IGS14 atx |

**Table 2.**Correlation coefficients between surface vertical deformation of water load in three filtered hydrological models and GRACE in SGN from 2010 to 2014.

Three Hydrological Models | CPC | WGHM | GLDAS |
---|---|---|---|

Correlation coefficient/NSE | 0.91/0.50 | 0.89/0.72 | 0.93/0.85 |

**Table 3.**Correlation coefficient and contribution rate between vertical time series from GNSS and load vertical deformation derived from GRACE in SGN from 2010 to 2014.

Different Method | GAC Correction | Without GAC Correction | ||
---|---|---|---|---|

Station Name | Correlation Coefficient | WRMS Contribution Rate/% | Correlation Coefficient | WRMS Contribution Rate/% |

GSJN | 0.89 | 52.79 | 0.55 | 16.53 |

GSJT | 0.63 | 18.75 | 0.33 | 3.65 |

GSLX | 0.88 | 45.59 | 0.65 | 21.18 |

GSPL | 0.83 | 43.97 | 0.62 | 20.20 |

NXZW | 0.78 | 31.48 | 0.22 | 2.37 |

SNAK | 0.79 | 37.92 | 0.09 | −8.42 |

SNMX | 0.89 | 54.82 | 0.53 | 13.45 |

SNTB | 0.58 | 18.52 | 0.10 | −5.72 |

**Table 4.**Statistical values of the vertical deformation from GNSS and the sum of GRACE and GAC in SGN from 2010 to 2014.

Station | GRACE | GNSS | ||
---|---|---|---|---|

Statistic | Annual Amplitude/mm | Annual Phase/rad | Annual Amplitude/mm | Annual Phase/rad |

GSJN | 4.30 ± 0.06 | −1.01 ± 0.03 | 5.61 ± 0.04 | −0.90 ± 0.01 |

GSJT | 3.60 ± 0.04 | −1.08 ± 0.02 | 3.47 ± 0.06 | −0.99 ± 0.03 |

GSLX | 4.80 ± 0.05 | −0.81 ± 0.02 | 7.03 ± 0.04 | −0.70 ± 0.01 |

GSPL | 4.99 ± 0.05 | −1.10 ± 0.03 | 5.78 ± 0.06 | −0.71 ± 0.01 |

NXZW | 5.00 ± 0.04 | −1.26 ± 0.01 | 8.00 ± 0.05 | −1.25 ± 0.02 |

SNAK | 5.12 ± 0.10 | −0.99 ± 0.04 | 6.94 ± 0.09 | −1.54 ± 0.03 |

SNMX | 5.15 ± 0.03 | −0.90 ± 0.03 | 5.46 ± 0.03 | −0.87 ± 0.02 |

SNTB | 4.62 ± 0.08 | −1.02 ± 0.04 | 3.30 ± 0.17 | −1.20 ± 0.10 |

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**MDPI and ACS Style**

Li, W.; Dong, J.; Wang, W.; Zhong, Y.; Zhang, C.; Wen, H.; Liu, H.; Guo, Q.; Yao, G.
The Crustal Vertical Deformation Driven by Terrestrial Water Load from 2010 to 2014 in Shaanxi–Gansu–Ningxia Region Based on GRACE and GNSS. *Water* **2022**, *14*, 964.
https://doi.org/10.3390/w14060964

**AMA Style**

Li W, Dong J, Wang W, Zhong Y, Zhang C, Wen H, Liu H, Guo Q, Yao G.
The Crustal Vertical Deformation Driven by Terrestrial Water Load from 2010 to 2014 in Shaanxi–Gansu–Ningxia Region Based on GRACE and GNSS. *Water*. 2022; 14(6):964.
https://doi.org/10.3390/w14060964

**Chicago/Turabian Style**

Li, Wanqiu, Jie Dong, Wei Wang, Yulong Zhong, Chuanyin Zhang, Hanjiang Wen, Huanling Liu, Qiuying Guo, and Guobiao Yao.
2022. "The Crustal Vertical Deformation Driven by Terrestrial Water Load from 2010 to 2014 in Shaanxi–Gansu–Ningxia Region Based on GRACE and GNSS" *Water* 14, no. 6: 964.
https://doi.org/10.3390/w14060964