In this article, two popular linear empirical methods viz., log-ratio model (LRM) and log-linear model (LLM) are used to derive water depths in shallow nearshore waters from Sentinel-2 multi-spectral images. Based on these empirical models, a multi-scene ensemble and a non-linear Support Vector Regression (SVR) machine learning approaches are applied to improve the accuracies from these traditional methods. In this analysis, firstly the best scene is selected from a set of six Sentinel-2 A&B images using noise-equivalent reflectance NEΔR_rs (sr⁻¹), optimal bands for LRM and LLM are selected using Optimal band ratio analysis (OBRA) and by computing Pearson Correlation Coefficient (R) between each band respectively. A total of 80% depth data points obtained from JetSki based echo-sounding measurements are used for training and the remaining 20% are used for testing each approach. The overall errors during the test phase for the range of depth 0–12 m are 0.79 m (0.67 m), 0.94 m (0.66 m) and 0.57 m (0.39 m) using traditional empirical LRM (LLM) methods from the best image, empirical-based ensemble and SVR approaches respectively. Irrespective of the approach, the LLM produced smoother and relatively accurate bathymetry as compared to the LRM. The LLM based SVR ML approach provides the best performance over the entire depth range as compared to all the methods considered in this study. Therefore, this method can be used for efficiently estimating nearshore depths and produce updated high-resolution bathymetry maps for many coastal applications.

在本文中，两种流行的线性经验方法，即对数比模型 (LRM) 和对数线性模型 (LLM) 用于从 Sentinel-2 多光谱图像中推导出近岸浅水区的水深。基于这些经验模型，应用多场景集成和非线性支持向量回归 (SVR) 机器学习方法来提高这些传统方法的准确性。在该分析中，首先使用噪声等效反射率 NEΔR _rs (sr ^-1)，分别使用最佳频带比分析 (OBRA) 和计算每个频带之间的皮尔逊相关系数 (R) 来选择 LRM 和 LLM 的最佳频带。从基于 JetSki 的回声测深测量中获得的总共 80% 的深度数据点用于训练，其余 20% 用于测试每种方法。使用传统经验 LRM (LLM) 方法从最佳图像得出的深度 0-12 m 范围的测试阶段的总体误差为 0.79 m (0.67 m)、0.94 m (0.66 m) 和 0.57 m (0.39 m)，分别基于经验的集成和 SVR 方法。不管采用哪种方法，与 LRM 相比，LLM 产生了更平滑和相对准确的水深测量。与本研究中考虑的所有方法相比，基于 LLM 的 SVR ML 方法在整个深度范围内提供了最佳性能。