Calculation of ocean environmental parameters from a Ka-Band scatterometer using the Longuet-Higgins approach

During the SAXON-FPN experiment in the North Sea off the coast of Germany, The University of Kansas operated a 35-GHz FM-CW Vector Slope Gauge (VSG) that simultaneously measured the range to three locations on the ocean surface. This enabled it to determine a time series of wave heights and time series of two orthogonal components of wave slopes. With this information, the wave-height spectrum, the directional spectrum, and the angular width spectrum can be determined. The authors calculate these parameters using the standard pitch-and-roll buoy technique and the VSG data [Longuet-Higgins et al., 1963]. They show simulations to illustrate inherent errors in the VSG measurements. The VSG measures the distance to a point along the radar beam, so the intersection with the surface does not move vertically. This introduces a phase shift in the time series of wave height and slope. Use of the average distance for the three beams to produce a single wave-height time series reduces the phase shift error. However, the slopes depend on differences in separate measurements of each range, so multibeam averages are impossible. In addition, the slope measurement is only a first-order approximation of the true slope, so errors result. Noiseless simulations of VSG performance for a simple ocean surface show that errors in the wave-height time series are relatively small. Similar simulations illustrate the errors in slope. Pitch-and-roll buoys also are subject to errors. The horizontal motion of the buoy must be accounted for, an effect similar to the slant-range errors of the VSG. The diameter of the buoy limits the length of ocean waves that can be accurately measured, a problem present with the VSG because of the finite size and spacing of the beams