The amplitude of internal solitary waves (ISWs) is a crucial parameter characterizing their properties. Leveraging machine learning and optical remote sensing images for ISW amplitude inversion has proven highly efficient. However, determining the best input features in the inversion model is often overlooked. This study addresses the feature selection problem in ISW amplitude inversion using a random forest (RF) method. The peak-to-peak distance and relative grayscale differences significantly influence ISW amplitude inversion. When solely using imaging features for ISW amplitude inversion, more significant errors are observed for low-amplitude ISWs due to their weak modulation. In amplitude inversion, selecting the dimensionless ISW amplitude for the output is necessary because it better represents the amplitude magnitude. We find that adding stratification parameters improves the inversion effect, especially the depth ratio. Thus, the impact of physical mechanisms on ISW amplitude inversion is pivotal, and incorporating more hydrological parameters as inputs would lead to further improvements in ISW amplitude inversion.

Achieving high-precision, high-resolution monitoring of nearshore water depth is essential for addressing marine disasters and environmental variations. Synthetic Aperture Radar (SAR) imaging offers the advantage of all-day, all-weather observations of coastlines, and imaging is unaffected by water quality. The current depth inversion methods typically exhibit an MRE of around 10%, with spatial resolution typically ranging from hundreds of meters to kilometers. However, Random Forest(RF) can leverage extensive data and complex algorithms to integrate the high resolution of SAR images and the high precision of in-situ data into the inversion model. To address this, we have employed ETOPO2022, multibeam bathymetric, and SAR images to create a depth inversion dataset comprising 542588 data points. In order to leverage this dataset effectively, we implemented an RF model for depth inversion from satellite images. During the model establishment process, ETOPO2022 data served as the primary training dataset, while high-precision multibeam data compensated for the limitations of low spatial resolution and low accuracy in shallow depths. The inversion model achieved a mean relative error (MRE) of 3.72% and a root mean square error (RMSE) of 2.28m on an independent dataset. When the model is applied to a larger area, the overall trend of the inversion results is accurate. Compared to reanalysis data, the inversion model exhibits higher spatial resolution, approaching 20m×22m. It is worth noting that the model demonstrates a strong inversion capability, especially in challenging shallow water areas. When accounting for extraction errors, the model demonstrated a considerable tolerance for errors.

The optical imaging mechanism of convex mode-2 Internal Solitary Waves (ISWs) in calm water without wind is investigated based on experimental and simulation calculations. By constructing an optical imaging system in the laboratory, the optical images of ISWs, the matching in-situ data, and the free surface displacement caused by ISWs are acquired simultaneously. The experimental outcomes show that the convex mode-2 ISWs exhibit bright-dark stripes in the optical image and produce a depressed free surface displacement on the water surface. The physical model of free surface displacement is constructed in Unigraphics NX (UG) and imported into Light Tools (LT) for ray tracing. The consistency between simulation calculations and experimental results shows that the free surface displacement generated by the mode-2 ISWs will change the reflection of light, leading to bright-dark stripes in the optical image. A series of experiments were designed to explore the influence of amplitude on the optical imaging of mode-2 ISWs when the thickness of the intermediate layer is different or the same. The results show that the amplitude of the wave will affect the imaging effect of ISWs in optical image, and the large amplitude will make the stripes clearer in the image.

Internal solitary waves (ISWs) cause changes in the flow field of a water column, which in turn excite convergent and divergent phenomena on the water surface. Due to the variation in wave elements and the complex marine environment, the optical remote sensing imaging of ISWs shows significant differences, which need to be further investigated. In this study, we propose a method that combines physical simulations with software simulations to investigate the optical imaging signals generated by ISWs. We designed three experiments based on the physical simulation platform to capture the convergent and divergent phenomenon and free surface displacement caused by ISWs. The influence of surface changes on imaging characteristics under different conditions was analyzed. The grayscale of ISW patterns with a high-density ratio deviates more from the background than those with a low-density ratio. In windy conditions, the imaging of convergent and divergent areas is more pronounced than that of surface waves and free surface displacement (FSD). Moreover, the bright-dark ratio of ISW patterns is mostly asymmetric. Next, we used software simulation to further explore the mechanism of optical remote sensing imaging of the ISWs. Different types of surface models were established using Unigraphics NX (UG) at the experimental scale to investigate the relationship between surface and imaging further. These models were imported into LightTools (LTs) to simulate the optical imaging. According to the sensitivity analysis of irradiance changes to wavelength and amplitude, one reason for the asymmetric bright-dark ratios is given. Finally, we find that the FSD only plays a certain role in imaging when the surface is calm. When ISWs modulate capillary waves, the convergent and divergent phenomena primarily influence imaging.

Optical remote sensing has been an important method to investigate the internal solitary wave (ISW). However, acquiring the ISW amplitude from optical remote sensing images has been the most difficult problem. In this letter, a method is proposed for inverting the amplitude of the ISW. A simulation platform of optical remote sensing is established to detect ISWs in the laboratory, which offers corresponding ISWs and remote sensing images. The experimental results show that the characteristic parameters of optical remote sensing images are changed with ISW amplitude. The relationship between them is nonlinear and related to the hierarchical structure. Hence, based on the support vector machine (SVM), random forest (RF), convolutional neural network (CNN), and multilayer perceptron (MLP), four inversion models of ISW amplitude are built and tested by the in situ data of the Wenchang area. The inversion results indicate that the average relative error of the SVM model is the smallest at 12.4%. It can be applied to the area with a ratio of stratification limited to 0.1-0.6.