**4. Discussion**

#### *4.1. Comparison with Precipitation over 10 River Basins*

It is verified that DWLIM can effectively derive the TWSA in mainland China, and it can detect the raised regions of the TWSA annual amplitude. The crust shows a decreasing trend when the terrestrial water storage load increases. On the contrary, the crust shows an upward rebound trend when the terrestrial water storage load decreases. This study combined monthly precipitation products provided by the China Meteorological Administration (CMA) to analyze the variation characteristics of regional TWSA in mainland China. Furthermore, this study extracted the precipitation and TWSA of 10 river basins in China based on boundary files. TWSA was calculated by DWLIM, and the comparison is shown in Figure 11.

**Figure 11.** The comparison of precipitation and TWSA over 10 basins in mainland China. (**a**) Yangtze River basin; (**b**) Southeast River basin; (**c**) Haihe River basin; (**d**) Huaihe River basin; (**e**) Yellow River basin; (**f**) Liaohe River basin; (**g**) Songhua River basin; (**h**) Northwest River basin; (**i**) Southwest River basin; (**j**) Pearl River basin.

Figure 11 indicates that the annual amplitude of TWSA is generally positively correlated with the annual amplitude of precipitation. The mean precipitation sequences in the Songhua and Liaohe River basins are significantly higher than the others. Correspondingly, the amplitudes of TWSA results are also significantly higher than those in the other basins. The phase relationship between TWSA and precipitation in mainland China shows good consistency. This further indicates the reliability of TWSA in phase for DWLIM inversion

in mainland China. However, the sequences of TWSA based on DWLIM and precipitation contain delays on the scale of months due to the time needed for the elastic deformation of TWSA. The results of TWSA and precipitation are consistent with previous studies [8]. The seasonal items of TWSA outcomes are more regular than previous TWSA results. Furthermore, the amplitude performance of TWSA and precipitation can also be used to evaluate the arid situation over the river basins. At the same time, it can also be seen that there is high-frequency noise in the time series of TWSA sequences, which also affects the inversion or prediction of TWSA. It is mainly caused by systematic noise from ionospheric, tropospheric, clock error, and multipath effects during GNSS observations [52,61]. Therefore, we will also focus on the noise classification and removal of GNSS vertical sequences to provide cleaner sequences for TWSA inversion in future research.

#### *4.2. Discussion of the Difference between Products*

In this study, we utilized DWLIM, GRACE, GLDAS, and the traditional GNSS method to calculate TWSA over mainland China. We compared these TWSA outcomes from the perspectives of spatial amplitude (Figure 8) and time series (Figure 9). It can be seen from Figure 8 that DWLIM is consistent with GRACE and GLDAS over most regions. However, there are also some differences between DWLIM and other products over certain regions, such as Beijing. The reasons for this can be summarized as follows. First, there are only two available GNSS stations (BJFS and BJSH) over Beijing. Second, vertical crustal deformation in the entirety of the North China Plain is complex and has been greatly influenced by human activity, which can cause inaccuracies in the simulated deformation. Third, the GNSS inversion result is also a little higher than the other products because the loaddeformation contains other components. Therefore, there may be some differences between the results of DWLIM and GRACE and GLDAS in some regions. Furthermore, it can be seen from Figure 8a,b that DWLIM can effectively suppress the speckle effect caused by uneven distribution of GNSS stations. In future research, we will focus on extracting cleaner crustal hydrological load-deformation to increase the accuracy of the inversion results.

#### **5. Conclusions**

The main research results can be summarized in the following three points.


Liaohe River basin are significantly higher than those in other basins. Furthermore, the wave peaks of precipitation are in good agreement with the peaks of TWSA, which are located in June or July. This result further verifies the reliability of the DWLIM inversion results in terms of phase.

**Author Contributions:** All authors collaborated to conduct this study; Y.S.: scientific analysis, manuscript writing, and editing. W.Z. and W.Y.: experimental design, project management, and review and editing. A.X. and H.Z.: review and editing. Q.W. and Z.C.: editing. All authors contributed to the article and approved the submitted version. Y.S., W.Z. and W.Y. contributed equally to this paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the National Natural Science Foundation of China (under grants 41774014 and 41574014), the Liaoning Revitalization Talents Program (under grants XLYC2002082, XLYC2002101, and XLYC2008034), the Frontier Science and Technology Innovation Project and the Innovation Workstation Project of Science and Technology Commission of the Central Military Commission (under grant 085015), and the Outstanding Youth Fund of China Academy of Space Technology.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors greatly appreciate the China Earthquake Administration for the GNSS data of Crustal Movement Observation Network of China (CMONOC: http://www.cgps.ac. cn, accessed on 9 December 2021) and the CSR (http://www.csr.utexas.edu/grace/, accessed on 6 August 2021) and JPL (https://grace.jpl.nasa.gov/, accessed on 9 December 2021), which provided the GRACE Mascon data. The authors would like to thank NASA for providing the dataset of GLDAS (http://agdisc.gsfc.nasa.gov/dods/, accessed on 9 December 2021). We thank ECMWF for providing the reanalysis data of the atmospheric pressure (https://www.ecmwf.int/, accessed on 21 December 2021). We thank the Earth system modeling group at Deutsches GeoForschungsZentrum for providing the corrected model (ESMGFZ: http://esmdata.gfz-potsdam.de:8080/repository/, accessed on 21 December 2021). We also thank China Meteorological Administration (CMA: http: //data.cma.cn/, accessed on 21 December 2021) for providing the precipitation data.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**

