## 5 Conclusions  
In this paper, we compare the seasonal VD time series derived from IG2, GRACE and GM solutions for 186 globally distributed IGS core stations over global region. We provide a thorough evaluation of the potential of two totally independent solutions to observe the non-tidal loading signal in GNSS, and also attempt to explain the remaining GNSS-GRACE/GM residuals. Our analysis can provide users with more clues to decide which model is better for their research when analyzing the seasonal signals over the global stations. The most meaningful analysis include two points: (1) we provide a thorough evaluation of the potential of two totally independent solutions (GRACE and GM) to observe the non-tidal loading signal in GNSS and (2) we investigate the noise properties of the GNSS corrected by GRACE solutions and GNSS corrected by GGFC solutions for global stations using optimal noise models. The results demonstrate the intrinsic relationship between GNSS and GRACE or GGFC vertical deformation mentioned above. After correcting the GNSS results with GRACE and GGFC loading deformations, the amplitude of the GNSS corrected by GGFC solutions is more optimal than the amplitude of the GNSS corrected by GRACE solutions, which may be owing to the filtering of the GRACE gravity field spherical harmonic coefficient preprocessing. The average of the correlation coefficients is 0.45 and 0.49 for GNSS vs. GGFC and GNSS vs. GRACE, respectively, indicating that GRACE loading deformations are more consistent with GNSS series. The mean value of the \(WRMS\) variations for all 186 stations is \(-\)12.3% and \(-\)5.6%, respectively, for GNSS vs. GRACE and GNSS vs. GGFC solutions. The GRACE correction improvement is generally better for the global stations and can be a more reliable choice when correcting the environmental loading deformation in GNSS stations around the world. Moreover, we introduce one further aspect that reflects the total effect of the related errors, namely the noise in the coordinate time series. Through the noise analysis with the optimal noise models, we can find that after subtracting the loading effects from the IG2 coordinate time series, the GNSS/GRACE solutions have the lowest noise level, demonstrating that the GNSS-GRACE combination solutions present more favorable results than that of GNSS-GGFC solutions. The GRACE deformations can occupy 5% of the noise behavior presenting in the global GNSS stations, while the GGFC results could bring more than 5% of the noise into the global stations. Finally, we revisit GRACE-derived loading deformation with GNSS station position time series in terms of the horizontal deformations, degree-1 coefficients effects and solutions from different institutions, and also try to perform comparisons with the previous research and detail the thermal expansion effects and leakage errors analysis. Our results display an improvement over the analyses presented by previous works, which may owe to the development of the GNSS data processing. Therefore, for the analysis of the surface loading effects on the global stations noise, the GRACE can provide better results for these research. Conceptualization, L.D. and H.C.; Methodology, L.D., Q.C. ; Software, L.D. ; Validation, L.D., and Q.C. ; Formal analysis, A.M., H.C.; Investigation, L.D. ; Resources, A.M., H.C.; Data curation, L.D. ; Writing--original draft preparation, L.D., H.C.; Visualization, A.M.; Funding acquisition, H.C. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Science Fund for Distinguished Young Scholars of China (Grant No. 41525014), the National Natural Science Foundation of China (NO. 41974019, 41704030), the Scientific Research Project of Hubei Provincial Department of Education (No. Q20194501), the Surveying and Mapping Basic Research Program of National Administration of Surveying, Mapping and Geoinformation (No.17-01-01) and Research Program of Hubei Polytechnic University (No.18 xyz09R).