Abstract
We propose an improved adjoint-based method for the reconstruction and prediction of the nonlinear wave field from coarse-resolution measurement data. We adopt the data assimilation framework using an adjoint equation to search for the optimal initial wave field to match the wave field simulation result at later times with the given measurement data. Compared with the conventional approach where the optimised initial surface elevation and velocity potential are independent of each other, our method features an additional constraint to dynamically connect these two control variables based on the dispersion relation of waves. The performance of our new method and the conventional method is assessed with the nonlinear wave data generated from phase-resolved nonlinear wave simulations using the high-order spectral method. We consider a variety of wave steepness and noise levels for the nonlinear irregular waves. It is found that the conventional method tends to overestimate the surface elevation in the high-frequency region and underestimate the velocity potential. In comparison, our new method shows significantly improved performance in the reconstruction and prediction of instantaneous surface elevation, surface velocity potential and high-order wave statistics, including the skewness and kurtosis.
Highlights
In recent years, with the increasing capabilities in water wave measurement, substantial efforts have been made to assimilate the observation data of water waves into computational models for wave field reconstruction and prediction
We have investigated the assimilation of measurement data for the wave field reconstruction and prediction based on the high-order spectral (HOS) method and its adjoint model
Compared with the conventional adjoint-based wave data assimilation method, free-parameter method (FPM), we have introduced a physical constraint on the initial wave field in the new method, connected-parameter method (CPM), which is shown to effectively reduce the cost function in both the reconstruction and prediction
Summary
With the increasing capabilities in water wave measurement, substantial efforts have been made to assimilate the observation data of water waves into computational models for wave field reconstruction and prediction. Shen techniques (Laxague, Curcic, Björkqvist, & Haus, 2017; Laxague, Zappa, LeBel, & Banner, 2018; Lund, Collins, Graber, Terrill, & Herbers, 2014; Lyzenga et al, 2015; Plant, Holland, & Haller, 2008). Data assimilation techniques, such as the Kalman filtering method and the adjoint method, are necessary to incorporate measured wave data into the numerical wave models when the required wave field information is not directly measured To reduce the negative impacts caused by these limitations, we propose an improved method to reconstruct the full phase-resolved wave field from the noisy measurement of wave surface elevation by utilising the adjoint method for data assimilation
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