Seawater depth information is of great significance for marine navigation, environmental monitoring, and seabed topography research. However, traditional depth measurement methods face difficulties in specific areas, such as remote waters and shallow regions. Satellite remote sensing depth measurement offers advantages such as wide coverage and cost-effectiveness, which makes it particularly suitable for the continuous monitoring of shallow marine areas and other regions that are difficult to reach with conventional field measurement methods. As a result, it has gained considerable attention. However, most existing remote sensing depth inversion models only use remote sensing reflectance as input features, which neglects the effect of water environmental factors on the results. To improve the accuracy and adaptability of depth inversion models, we introduce the chromaticity angle as a new feature and combine machine learning techniques to enhance the precision and applicability of existing remote sensing depth inversion methods, thereby providing effective technical support for remote sensing depth inversion in shallow marine areas.

We introduce the chromaticity angle as a new feature and combine it with remote sensing reflectance data to develop a shallow water depth inversion model using three machine learning algorithms: random forest (RF), extreme gradient boost (XGB), and support vector regression (SVR). First, Sentinel-2 satellite imagery is used to collect water reflectance data, and the chromaticity angle is calculated as an additional feature. This angle effectively captures the optical properties of the water, compensating for the limitations of using only reflectance in traditional remote sensing methods. Then, machine learning models are built using both the reflectance and chromaticity angle data for depth inversion. RF handles nonlinear relationships by constructing multiple decision trees, while SVR excels in dealing with small sample sizes and high-dimensional data. XGB, an advanced ensemble algorithm, iteratively optimizes the model’s performance for complex regression tasks. The inversion accuracy of the models is assessed using metrics such as root mean square error (RMSE), mean absolute error (MAE), and mean relative error (MRE). Additionally, Shapley additive explanations (SHAP) values are applied to analyze the contribution of each feature variable to the model’s output, which further confirms the significant role of the chromaticity angle in improving inversion accuracy.

After combining the chromaticity angle with the remote sensing reflectance data, the accuracy of the shallow water depth inversion model is effectively improved. The comparative analysis of the three machine learning algorithms indicates that the improved XGB model performs the best, with an RMSE of 1.11 m, MAE of 0.81 m, and MRE of 11.05% (Table 2), which demonstrates a clear advantage over traditional empirical algorithms. Additionally, the XGB model exhibits robust inversion performance in areas with steep depth gradients (Fig. 9). The scatter plot demonstrates that the chromaticity angle enhances the correlation between predicted and observed values and improves the coefficient of determination R2 (Fig. 5). Residual analysis shows that the application of the chromaticity angle feature results in a more concentrated distribution of residuals, with smaller deviations between predicted and observed values (Figs. 6 and 7). Compared to other depth ranges, the effect of the chromaticity angle is more significant in the deeper water range of 15?25 m (Table 3). SHAP analysis quantifies the contribution of each input variable to the model, which confirms that the chromaticity angle feature is a crucial predictor of water depth and has a more substantial impact in deeper waters (Fig. 10).

We propose a shallow water depth inversion method assisted by the chromaticity angle based on machine learning. The chromaticity angle is calculated from the remote sensing reflectance of the red (R), green (G), and blue (B) bands as a new inversion feature to improve the accuracy of satellite bathymetry. The method is applied and validated using three machine learning models: RF, XGB, and SVR. The results show that incorporating the chromaticity angle as an input feature can effectively enhance the predictive performance of the machine learning models. Among them, the improvement in the RF model is the most significant, while the XGB model, combined with the chromaticity angle, achieves the best performance. Compared to other machine learning algorithms and traditional empirical methods, this approach demonstrates clear advantages and higher fitting accuracy in areas with steep depth changes, which exhibits excellent water depth inversion performance. A depth-segment analysis reveals that the effect of the chromaticity angle is more pronounced in waters deeper than 15 m. Additionally, since the calculation of the chromaticity angle is based on widely available remote sensing imagery data, the proposed method has great potential for application in different geographic regions.