Modeling of water waves and sediment transport using physics-based and machine learning methods

Abstract

Accurate information about nearshore waves and sediment transport is essential for designing and operating many coastal projects, such as wetland restoration, flood protection, port and harbor development, and coastal zone management. However, in-situ measurements are usually spatially and temporally sparse and time-consuming to achieve. Thus, various models have been developed to simulate nearshore waves and sediment transport, such as physics-based and machine learning models. For physics-based models, there has been considerable progress in predicting nearshore waves and sediment transport by solving the action balance equation, momentum balance equation, and advection-diffusion equation with the finite difference, finite element, or spectral methods during the past three decades. Considering the sensitivity of meshing a complicated geometry and the difficulty of creating nested computational domains, high-fidelity physics-based models can be computationally prohibitive for many real-world complex applications. Recently, the development of machine learning theory, computer hardware, and remote sensing technologies have created new opportunities for using soft computing-based models to explore nearshore wave fields and morphological changes. In this work, we develop four types of models to simulate/reconstruct wave fields and investigate the spatial and temporal characteristics of sediment transport in shallow waters. The objective is five-fold: (1) to simulate wave fields and sediment transport in a connected river-estuary-ocean system with physics-based models, (2) to estimate wave parameters with data-driven models in an estuary, (3) to simulate nearshore waves with hybrid methods by combining physics-based and data-driven models and identify sources of error in physics-based models, (4) to reconstruct wave fields with physics-informed machine learning models, and (5) to solve the surf zone bathymetric inversion problem with physics-informed neural networks. Firstly, a coupled flow-wave Delft3D model was developed to study hydrodynamics and sediment transport in Fourleague Bay of the Mississippi River Delta and explore effective strategies for designing and implementing sediment diversions for wetland restoration and coastal resilience to sea level rise. We found that the riverine sediment tended to be directly deposited in the marshes when the river discharge was high with strong northerly winds at the study site. During calm weather, the riverine sediment was more likely to be deposited into the bay floor first, which was later resuspended and transported to the marshes during storms. It is therefore important to retain sediments from river divisions in shallow bays and allow storms to redistribute them to adjacent wetlands in a deltaic environment. Secondly, we developed soft computing-based models to estimate long-term wind wave characteristics across a living shoreline project with constructed oyster reefs (CORs) in Delaware Bay based on short-term field measurements during storms. This enabled us to determine the wave power variation across the living shorelines on a yearly basis. It was found that when the CORs were emergent or slightly submerged, the averaged wave height attenuation was about 39.8% from the offshore gauge to the nearshore gauge (behind CORs) during 2018-2020, owing to the combined effect of nearshore bathymetric changes and CORs. This study provides a novel framework to predict long-term wave characteristics based on short-term wave measurements using machine learning models. Thirdly, we integrated the physics-based model with machine learning models to estimate wave parameters in a shallow estuary in the Mississippi River Delta and identified the main factors causing simulation errors in physics-based wave models. The results show that the wind direction and bottom friction coefficient were the main factors causing errors in the physics-based modeled significant wave height and peak wave period, respectively. We showed that the developed hybrid approach could be an efficient tool for modelers to identify sources of error and calibrate parameters in physics-based models. Fourthly, a novel PINN (physics-informed neural network) model was developed to reconstruct wave fields in shallow waters with scarce wave measurements by combining prior knowledge into the soft-computing learning algorithm. The model performance is examined by comparing the PINN outputs with numerical solutions from a physics-based model and experimental data over a two-dimensional alongshore uniform barred beach and a three-dimensional circular shoal, respectively. Our results show that the physics-guided deep learning method is a promising tool for studying nearshore processes. Fifthly, we developed an inverse PINN model to determine the nearshore bathymetry based on remote sensing or in-situ data. The results showed that PINNs could well estimate both the bathymetry and wave fields with a much smaller amount of training data than pure ANN models. Moreover, we found that the effect of wave nonlinearity (i.e., amplitude dispersion) on depth inversion and wave field prediction can be incorporated into the models, which is one of the advantages of using PINNs to solve bathymetry inversion problems. Overall, our results show that the inverse PINN model is a promising tool for estimating nearshore water depth based on observations from various sensing platforms.--Author's abstract