Calculation of the microwave refractivity traditionally depends on the vertical gradients of temperature and humidity. It is shown herein that if there are horizontal gradients of the momentum, heat, and moisture flux between the air and sea (or alternatively the horizontal gradients of the roughness lengths for these fluxes), the refractivity exhibits a strong dependence on fetch. The equations were demonstrated using typical environmental meteorological data, typical wave spectra, and differences between the refractivity and duct strength are calculated both with and without the terms involving horizontal gradients. In general, for offshore flow the ducts are deeper and radius of curvatures are smaller as one moves closer to the shore from distances far offshore.
Gerald L. Geernaert,
"Refractivity gradients in the coastal zone", Proc. SPIE 2828, Image Propagation through the Atmosphere, (14 October 1996); doi: 10.1117/12.254159; https://doi.org/10.1117/12.254159