Optimal Experimental Design of Sensor Locations in EnKF Data Assimilation for Predicting Oceanic Rogue Waves

Abstract:

The phase-resolved prediction of ocean waves, especially the rogue waves, is crucial for the safety of offshore operations. However, errors in the initial condition (associated with the radar measurements and reconstruction algorithm) and the chaotic nature of the nonlinear wave equations render wave predictions to quickly deviate from the true surface evolution. Consequently, the onset of rogue waves often cannot be reliably detected. To address this issue, it is necessary to incorporate measured data into the simulation via data assimilation (DA), and optimize the data collection (sensor) location to improve the performance. In this study, we combine optimal experimental design of sensor locations with a newly developed and validated ensemble Kalman filter (EnKF) – high order spectral (HOS) coupled algorithm for predicting oceanic rogue waves. We simulate the phase-resolved wave field with DA at different candidate sensor locations and optimize a goal-oriented expected error on rogue wave quantities of interest. Specifically, this objective involves the absolute error of the ensemble mean on the predicted wave height at the desired ocean structure location, and taken in expectation over the initial ensemble distribution and over different realizations of the observation noise. Demonstrating for a one-spatial-dimension problem, we first present results on a 1-probe design together with discussions from the wave physics, and then employ Bayesian optimization to find multi-sensor configurations.