Effect of the One-to-Many Relationship between the Depth and Spectral Profile on Shallow Water Depth Inversion Based on Sentinel-2 Data

Abstract

In shallow water, Sentinel-2 multispectral imagery has only four visible bands and limited quantization levels, which easily leads to the occurrence of the same spectral profile but different depth (SSPBDD) phenomenon, resulting in a one-to-many relationship between water depth and spectral profile. Investigating the impact of this relationship on water depth inversion models is the main objective of this paper. The Stumpf model and three machine learning models (Random Forest, Support Vector Machine, and Mixture Density Network) are employed, and the performance of these models is analysed based on the spatial distribution of the training dataset and the input information composition of these models. The results show that the root mean square errors (RMSEs) of the depth inversion of Random Forest and Support Vector Machine are significantly affected by the spatial distribution of the training dataset, while minimal effects are observed for the Stumpf model and the Mixture Density Network model. The SSPBDD phenomenon is widespread in Sentinel-2 images at all depths, particularly between 5 m and 15 m, with most of the depth maximum difference of the SSPBDD pixels ranging from 0 to 5 m. The SSPBDDs phenomenon can significantly reduce the inversion accuracy of any model. The number and the depth maximum difference of the SSPBDDs pixels are the main influencing factors. However, by increasing the visible spectral information and the spatial neighbourhood information in the input layer of machine learning models, the inversion accuracy and stability of the models can be improved to a certain extent. Among the models, the Mixture Density Network achieves the best inversion accuracy and stability.

Keywords

• depth inversion
• mixture density network (MDN)
• same spectral profile but different depth (SSPBDD)