## 6 Conclusions  
This study proposes a high-resolution water depth inversion method based on GF-1 satellite data, utilizing the scale-invariant effect to successfully achieve water depth inversion at a spatial resolution of 2 m. This method not only enhances the spatial resolution of bathymetry mapping but also provides an innovative solution for the economical and efficient mapping of underwater topography. The research results indicate that, compared to the water depth results derived from Sentinel-2 data, the water depth data inverted from GF-1 exhibit a similar overall trend. Although there are instances of underestimation at the edges of certain islands, the GF-1 data present a more detailed and richer depiction of local water depth features. Furthermore, the accuracy was evaluated by comparison with ICESat-2 data. The results showed that the \(R^{2}\) values of the four study areas were all greater than 0.85, the RMSE ranged from 0.56 to 0.90 m, with an average of 0.7125 m, and the MAE ranged from 0.43 to 0.76 m, with an average of 0.55 m, which further verified the reliability of this research method in water depth inversion. In addition, this study also explores the applicability of the scale-invariance assumption and compares the effect of using the QPRM to replace the traditional CLRM, and the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Study Area** & \(R_{0}^{2}/R_{L}^{2}\) & \(RMSE_{Q}/RMSE_{L}\) & \(MAE_{Q}/MAE_{L}\) \\ \hline Vuthovitho Island & 0.9475/0.9429 & 0.69/0.72 & 0.52/0.55 \\ Onotoa Island & 0.9424/0.9288 & 0.90/1.01 & 0.76/0.86 \\ Ant Atoll & 0.9340/0.9313 & 0.70/0.96 & 0.49/0.71 \\ Emae Island & 0.8797/0.8765 & 0.56/0.61 & 0.43/0.48 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The table presents a comparison of the fitting results between the CLRM and the QPRM, where the subscript “Q” denotes the fitting results of the QPRM and the subscript “L” denotes the fitting results of the CLRM. results show that QPRM demonstrates a significant improvement within the framework of this study, which further proves the effectiveness and innovation of the proposed method and demonstrates the promising prospect of the GF-1 satellite data in bathymetric mapping. However, this study does have some limitations. Firstly, due to the temporal resolution of the GF-1 satellite and the climatic conditions characterized by frequent cloud cover and rain in the Pacific Island region, the number of effective images from the GF-1 satellite in the Pacific area is quite limited. This study exclusively employed single-scene GF-1 imagery for bathymetric inversion. It should be noted that the accuracy of such single-scene-derived results is inherently constrained by image quality factors, which may introduce certain uncertainties. Second, the current preprocessing methods for GF-1 satellite data are not well developed, lacking a systematic and dedicated approach for quality control specific to this satellite series. This may affect both the image quality and the final water depth inversion results. To address these issues, future research could focus on developing more comprehensive image quality control and preprocessing methods or exploring multi-temporal data fusion techniques to enhance the quality of remote sensing imageries and improve the accuracy of water depth inversions. On the other hand, since the study area of this research is primarily focused on Pacific Island countries, and there is a lack of extensive and reliable in situ bathymetric data in this region, the research results presented in this paper could not be directly validated against in situ bathymetric data. Therefore, we could only refer to previous water depth inversion results and ICESat-2 data to assess the feasibility of the methods employed in this study. Nevertheless, the research indicates that this method has strong application potential, and future studies could be conducted in more regions, incorporating in situ data to validate and optimize the method, thereby enhancing its applicability and accuracy.