The relief and roughness of natural surfaces interacting with airflows and with radiation affect rates and distributions of heat and vapor fluxes into the atmosphere. The study quantifies interactions of regular sinusoidal wavy porous surfaces (with different geometrical characteristics) affecting heat and vapor transport into prescribed turbulent airflows. A model for turbulent eddies interacting with an undulating evaporating surface with mean boundary layer that varies across sinusoidal wavy surfaces was developed and experimentally evaluated in a wind tunnel. The surface of a shallow (0.3 m deep) sand-filled basin was imprinted with regular sinusoidal ridges and troughs; water content and temperature sensors were embedded in the sand, and the instrumented basin was placed on a balance in the wind tunnel. Detailed thermal signatures of the evaporating surface for different wind speeds and surface patterns were obtained using high-resolution infrared thermography. The evaporative mass loss measurements and observed thermal patterns were in good agreement with model predictions for turbulent exchange over various wavy sand surface geometries. Results suggest that evaporative fluxes can be either enhanced or suppressed (relative to a flat surface) due to complex interplay between local boundary layer thickness and internal limitations to water flow to the evaporating surface. For a practical range of air velocities (0.5-4.0 m/s), and for sinusoidal configurations studied (amplitudes of 50-100 mm), the evaporative mass loss (relative to the flat surface) was reduced by up to 60 % for low surface aspect ratio and high wind velocity, and enhanced by up to 80 % for high aspect ratio and low wind velocity. The study offers a framework for interpreting and upscaling evaporative fluxes from rough terrestrial surfaces. Ongoing work considers shortwave radiation and geometrical interactions for a more complete account of surface energy balance and fluxes from natural rough surfaces.