The dynamic topography of wind-generated gravity-capillary waves retrieved from color images

The smooth surface of calm water is disrupted by wind to create a dynamic topography of propagating waves with wavelengths spanning millimeters to hundreds of meters on the open ocean. Under certain wind conditions, the leeward faces of long gravity waves become covered by patches of short "parasitic" gravity-capillary waves in a coherent manner. Gravity-capillary waves have wavelengths that are similar to microwaves and these patches can act as "tilted Bragg gratings", causing interference and Doppler effects that are exploited for the remote sensing of sea surface wind speed and direction and water current by microwave scatterometry. Detailed measurements of the dynamic topography of wind-generated waves would provide surface realizations useful in simulations of electromagnetic interaction with the ocean surface and to provide deeper insight into the coherent nature of short and long wavelength water waves.;In this dissertation, the dynamic topography of short wind-generated waves in the gravity-capillary regime is measured using high speed color image sequences of light from a structured source that is distorted by refraction through the wavy surface. Surface topography is retrieved from color images using a nonlinear forward model of image formation to enable comparison of a trial surface topography with image data, a method of slope estimation for locations on the surface corresponding to each pixel, and a method of topographic retrieval from slope estimates using a direct solution of a sparse weighted system of linear algebraic equations. Retrieval results reveal the evolving surface topography in fine detail, providing an explicit surface representation on sub-millimeter to decimeter length scales. The results clearly reveal the coherent relationship between short and long water waves. Topographic retrievals covering wind conditions from 0 to 12 m s-1 with 8 m fetch in a wind wave tank form a data set of surface realizations that may be used to improve models of electromagnetic interaction with ocean surfaces.