Hydrodynamic modulation of short wind‐wave spectra by long waves and its measurement using microwave backscatter

In this paper we use results of microwave backscattering experiments over the past decade to attempt to present a coherent picture of the ocean wave-radar modulation transfer function (MTF) based on composite surface theory, short-wave modulation, and modulated wind stress. A simplified relaxation model is proposed for the modulation of the gravity-capillary wavenumber spectrum by long waves. The model is based on the relaxation rate and the equilibrium gravity-capillary wavenumber spectrum. It differs from previous models by including all airflow modulation effects in the response of the equilibrium spectrum to changes in the airflow. Thus the explicit modulation of individual source functions such as wind input, short-wave dissipation, and nonlinear interactions need not be known in order to calculate the hydrodynainic MTF. By combining this new model of the hydrodynamic MTF with microwave measurements, we attempt to determine wind shear stress modulation caused by the long waves. In order to extract the hydrodynamic MTF from the microwave data, we remove tilt and range change effects from the measured MTFs using the published analytical forms for these effects. Our results show that the inferred hydrodynamic MTF is higher for II polarization scattering than for V polarization. Since this is impossible if we have obtained the true hydrodynamic MTF, these results strongly indicate a problem with composite scattering theory as it has been traditionally applied. One explanation for this result may be the effects of intermediate-scale waves suggested by Romeiser et al. (1993). Since these effects are much stronger for H polarization than for V polarization, they may explain our observed discrepancy and, if so, imply that V polarization return should yield an acceptable upper limit for the true hydrodynamic MTF. Thus we incorporate our V polarization results into the proposed model to estimate an upper limit for the wind shear stress modulation along the long-wave profile. We infer that the primary source of modulation of Bragg resonant waves depends strongly on Bragg wavenumber and windspeed. For low values of these quantities, straining by long-wave orbital velocities dominates the modulation process, while for higher values modulated wind stress becomes increasingly important. Our calculations indicate that wind stress modulation dominates the process for 3 cm Bragg waves at moderate to high wind speeds.