Relationship Between Wave-Related Reynolds Number and Doppler Velocity at Grazing Incidence

We show empirical evidence that the mean spatial gradient of the Doppler velocity, measured by a coherent X-band marine radar at grazing incidence, serves as a reliable proxy for measuring the so-called wave-related Reynolds number - defined as the product of air-side friction velocity and significant wave height divided by the kinematic viscosity of the surface water. Comparisons to approximately 180 hours of in situ observations spanning various environmental conditions in the Southern North Sea yield an overall squared correlation coefficient of 0.93, and a normalized root-mean-square error of 16%. These results suggest that coherent marine radar offers a practical and relatively cost-efficient tool for observing key parameters related to ocean surface dynamics and air-sea interactions, such as whitecap coverage.