Adjoint-based Data Assimilation for Ocean Waves

Abstract

The exchange between the atmosphere and oceans, which regulates weather and climate processes and upper ocean dynamics, critically depends on the spatial and temporal evolution of ocean surface waves. In reality, directly measuring the entire wave state is an expensive and difficult task. Firstly, we propose a method for the reconstruction and prediction of nonlinear wave fields from coarse-resolution measurement data. We adopt the adjoint-based data assimilation framework to search for the optimal wave states to match the given measurement data and governing physics. The performance of our method is assessed by considering a variety of wave steepness and noise levels for the nonlinear irregular wave fields. It is found that our method shows significantly improved performance in the reconstruction and prediction of instantaneous surface elevation, surface velocity potential, and high-order wave statistics. Secondly, we propose a method to infer coastal bathymetry from the spatial variations of surface waves by combing a high-order spectral method for wave simulation and an adjoint-based variational data assimilation method. The proposed bottom detection method is applied to a realistic coastal environment involving complex two-dimensional bathymetry, non-periodic incident waves, and nonlinear broadband multi-directional waves. We also address issues related to surface wave data quality, including limited sampling frequency and noise. Both laboratory-scale and field-scale bathymetries with monochromatic and broadband irregular waves are tested, and satisfactory detection accuracy is obtained. Last, we investigate the impact of oceanic internal wave and surface wave parameters on the surface roughness signature based on the two-fluid solver. We use the ratio of the mean surface slope between the rough and smooth bands, which are identified in the simulated surface field, to systematically investigate their response to the internal wave forcing across all our simulation cases. We find that the strongest surface heterogeneity is caused by varying upper-lower layer density ratios. Our results also show that it is necessary to include the wave steepness statistics to account for the internal wave-induced surface wave modulation.