Wavenumber Dependence of the Response Time of Mean-Square Slope to Wind Forcing

The motivation for this work lies in the bistatic remote sensing of ocean surface windspeed using L-band GPS signals, which has been proposed as an alternative to microwave radiometry and monostatic radar scatterometry. L-band forward-scattered signals are dominated by the quasi-specular reflections dependent on the mean-square slope, which, in turn, is affected by longer wavelengths than those sensed by conventional radiometers and scatterometers. It is known that longer surface waves take more time to respond to surface winds, propagate further before decaying, and are generally less directly coupled to the local wind field. In this work, we attempt to quantify the response time of the longwave spectrum to local winds by examining windspeed and surface slope measurements made by several buoys. By applying a lag-correlator, it is observed that the average lag time decreases monotonically as a function of wavenumber. Because buoys have an upper limit in the wavenumber range it can sense, a conservative upper bound of about 1 hour is found to be the average response time of L-band mean-square slope to wind forcing.