A Synergistic Remote Sensing Inversion Study of Water Depth in Inland Lakes Integrating Chlorophyll-a Concentration and Optical Indices

Accurate bathymetric information for inland lakes is essential for water resource management, ecological monitoring, and environmental research. However, the accuracy and robustness of remote sensing-based bathymetric retrieval are often constrained by the complex optical properties of inland waters and the limited representation of conventional inversion features. To address these challenges, this study systematically compared the performance of a multiband logarithmic ratio model and three machine learning models, including Random Forest (RF), XGBoost, and AdaBoost, for inland lake bathymetric retrieval. Furthermore, a synergistic retrieval framework integrating chlorophyll-a concentration (Chla) and a Water Optical Index (WOI) was proposed. The results show that: (1) The overall accuracy of the Random Forest, XGBoost, and AdaBoost models constructed with the integration of chlorophyll-a concentration and WOI ($R^2=0.93$, $0.93$, and $0.91$; MAE $=0.06$ m, $0.07$ m, and $0.12$ m; RMSE $=0.14$ m, $0.14$ m, and $0.16$ m) outperforms that of models using only multispectral band information ($R^2=0.93$, $0.91$, and $0.82$; MAE $=0.06$ m, $0.07$ m, and $0.14$ m; RMSE $=0.14$ m, $0.16$ m, and $0.22$ m). Moreover, all these machine learning models significantly outperform the traditional numerical model ($R^2=0.27$; MAE $=0.29$ m; RMSE $=0.45$ m), with the Random Forest model achieving the best overall performance. This indicates that the proposed method offers higher applicability and retrieval accuracy in complex inland lake environments. (2) The optimal Random Forest model integrating chlorophyll-a concentration and WOI achieved high-precision bathymetric inversion for inland lakes ($R^2=0.93$, MAE $=0.06$ m, RMSE $=0.14$ m). Based on the three-dimensional bathymetry derived from this model, the estimated lake storage capacity was $1072.11\times {10}^4$ m³, compared with a measured volume of $1094.27\times {10}^4$ m³, yielding a relative error of $-2.03\%$. This result provides reliable and highly accurate data to support water resource management.