*4.3. Limitation and Furture Work*

In this study, there are some limitations, although reasonable results have been achieved. First, the GWFM proposed in this study is based on the same assumptions as the ETC method, such as error orthogonality and zero-error cross-correlation. Second, this study only uses GLDAS, ERA5, and WGHM, without considering other data sources. Third, there is only an eight-year overlap period with the GRACE data due to the short and discontinuous in situ groundwater-level measurement data. It is impossible to test the performance of the GWFM over a longer time frame.

In follow-up work, more data will be introduced to develop the model to compare and analyze GWSA in arid regions where in situ groundwater-level measurements are scarce. Furthermore, we will conduct a comparative analysis with the existing multi-model combination of technology to further improve the GWFM.

#### **5. Conclusions**

This study estimates GWSA by combining GRACE data with hydrological models. These data have their own unique characteristics and are developed for a global scale. Therefore, estimation of regional water-storage state generated by a single model may have greater uncertainty. In response to this problem, a GWFM is presented that can merge multi-source GWSA. The useful conclusions are as follows:


**Author Contributions:** All authors collaborated to conduct this study. K.S., formal analysis, manuscript writing, and editing; W.Z. and W.Y.: supervision, project management, and editing; L.H. and Y.S., review and editing. 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 Grant (41774014, 41574014), the Liaoning Revitalization Talents Program under Grant (XLYC2002082), 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:** No new data were created or analyzed in this study. Data sharing is not applicable to this article.

**Acknowledgments:** The authors greatly appreciate the institutions of CSR (http://www.csr.utexas. edu/grace/ (accessed on 1 July 2021)), which provided the GRACE mascon data. The authors would like to thank NASA for providing the dataset of GLDAS (https://disc.gsfc.nasa.gov/ (accessed on 1 July 2021)). The authors thank ECMWF (https://www.ecmwf.int/ (accessed on 1 July 2021) for the re-analysis data of the atmospheric pressure. The authors thank Hannes Muller Schmied for providing the hydrological outputs from the WGHM model. Finally, the authors also thank China Meteorological Administration (http://data.cma.cn/ (accessed on 10 August 2021)) for providing precipitation dataset. Kai Su, Wei Zheng, and Wenjie Yin contributed equally to this paper.

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