Date of Award
Master of Science in Coastal Marine and Wetland Studies
Coastal and Marine Systems Science
Erin E. Hackett
Phase-resolved ocean surface wave elevation maps provide important information for many scientific research areas (e.g., rogue waves, wave-current interactions, and wave evolution/growth) as well as for commercial and defense applications (e.g., naval and shipping operations). To produce these maps, measurements in both time and space are necessary. While conventional wave sensing techniques are limited spatially, marine radar has proven to be a complex yet promising remote sensing tool capable of providing both temporal and spatial wave measurements. The radar return from the sea surface is complex because it contains contributions from many sources only part of which provide information about the ocean surface wave field. Most existing techniques used to extract ocean wave fields from radar measurements implement fast Fourier transforms (FFTs) and filter this energy spectrum using the linear dispersion relationship for ocean waves to remove non-wave field contributions to the radar signal. Inverse Fourier transforms (IFFTs) return the filtered spectrum to the spatial and temporal domain. However, nonlinear wave interactions can account for a non-negligible portion of ocean wave field energy (particularly in high sea states), which does not completely adhere to the linear dispersion relationship. Thus, some nonlinear wave energy is lost using these FFT dispersion-filtering techniques, which leads to inaccuracies in phase-resolved ocean surface wave field maps. This deficiency is significant because many of the aforementioned research areas and applications are most concerned with measurement and prediction of such anomalous wave conditions. Proper orthogonal decomposition (POD) is an empirical technique used in scientific fields such as fluid mechanics, image processing, and oceanography (Sirovich, 1987). This technique separates a signal into a series of basis functions, or modes, and time or spatial series coefficients. Combining a subset of the modes and coefficients can produce a reduced order representation of the measured signal; this process is referred to as a reconstruction. This research applies POD to radar Doppler velocity measurements of the sea surface and uses the leading modes as a filter to separate wave contributions to the radar measurement from non-wave contributions. In order to evaluate the robustness of this method, POD is applied to ocean wave radar measurements obtained using three different radar systems as well as to numerically modeled radar data for a variety of environmental conditions. Due to the empirical nature of the POD method, the basis functions have no innate physical significance, therefore the shape and content of leading POD modes is examined to evaluate the linkage between the mode functions and the wave field physics. POD reconstructions and FFT-based methods are used to compute wave field statistics that are compared with each other as well as to ground truth buoy measurements. Correlation coefficients and root mean squared error are used to evaluate phase-resolved wave orbital velocity time series reconstructions from POD and FFT-based methods relative to ground truth buoy velocity time series measurements. Results of this study show that when POD is applied to radar measurements of the sea surface: (i) the leading mode basis functions are oscillatory and linked to the physics of the measured wave field; (ii) POD performs comparably to FFT-based dispersion filtering methods when calculating wave statistics; and (iii) phase-resolved POD orbital velocity maps show higher correlations with buoy velocity time series relative to orbital velocity time series based on FFT dispersion filtering methods when high group line energy is present (i.e., in the presence of steep and breaking waves).
Kammerer, Andrew Joseph, "The Application of Proper Orthogonal Decomposition to Numerically Modeled and Measured Ocean Surface Wave Fields Remotely Sensed by Radar" (2017). Electronic Theses and Dissertations. 26.