Proper Orthogonal Decomposition Applied to Numerically Modeled and Measured Ocean Surface Wave Fields Remotely Sensed by Marine Radar

In many oceanic applications, it would be advantageous to know the phase resolved surface wave field, which requires measurement in both time and space. Marine radar has proven to be a complex, yet promising tool, capable of providing temporal and spatial wave measurements - in contrast to conventional wave sensors, such as buoys, that make point measurements over time. Most current methods of processing radar data to extract the ocean wave field consist of using fast Fourier transforms (FFTs) and filtering the resulting energy spectrum using the linear dispersion relationship to remove non wave field contributors to the radar signal. Inverse Fourier transforms (IFFTs) return the filtered spectrum to the spatiotemporal domain. However filtering on the linear dispersion relationship removes nonlinear wave energy, including wave breaking, from phase resolved wave fields. Proper orthogonal decomposition (POD) is a technique used to provide low-dimensional representations of high-dimensional systems and has been applied extensively in nonlinear applications such as turbulence. Previous studies have shown consistency in POD modes as well as a linkage to the physics of the wave field for simple sinusoidal and Bretschneider spectral wave models. Results of this study show POD applied to measured and modeled radar measurements of the sea surface for estimating the wave field in comparison to traditional approaches. POD applied to spatiotemporal radar data shows the leading order modes (approximately the first 25 modes) contain the majority of the energy in peak wavenumber/frequency bands at levels that are greater or equivalent to that retained using dispersion curve filtering. This retained energy is located both on and off the dispersion curve. POD reconstruction of phase resolved wave fields using modeled radar measurements of a known sea surface allow for quantitative evaluation of the accuracy of the POD technique in comparison to traditional approaches.