Rates of gas transfer between air and water remain difficult to predict or simulate due to the wide range of length and time scales and lack of experimental observations of near-surface fluid velocity and gas concentrations. The surface renewal model (SR) and surface divergence model (SD) provide the two leading models of the process, yet they remain poorly tested by observation because near-surface velocity is difficult to measure. To contribute to evaluation of these models, we apply new techniques called interfacial particle imaging velocimetry (IPIV) and three-dimensional IPIV (3D-IPIV) for measuring water velocities within a millimetre of a moving deformable air–water interface. The latter technique (3D-IPIV) simultaneously measures the air–water interface topography. We apply these techniques to turbulent open-channel water flows and wind-sheared water flows with microscale breaking waves. Additional measurements made for each flow condition are bulk turbulent length scales, bulk turbulent velocity scales, air–water gas transfer rates, friction velocities, and wave characteristics. We analyse these data to test the surface divergence models for interfacial gas transfer. The first test is of predictions from the Banerjee (Ninth International Heat Transfer Conference, Keynote Lectures, vol. 1, 1990, pp. 395–418, Hemisphere Press) surface divergence model for gas transfer for homogeneous isotropic turbulence interacting with a planar free surface. The second test is of predictions from the McCready, Vassiliadou and Hanratty (AIChE J., vol. 32(7), 1986, pp. 1108–1115) surface divergence model, as applied in both open-channel flow and wind-sheared wavy flows. We find the predictions of the Banerjee and McCready et al. models to agree with the experimental data taken for open-channel flow conditions. On the other hand, for wind-driven flows with wind waves we find disagreement between the McCready et al. predictions and our direct measurements of the gas transfer coefficient. The cause of the disagreement is investigated by Lagrangian tracking of surface divergence of surface water patches, and by analysis of the corresponding Lagrangian time series with advection–diffusion concepts. A quantitative criterion based on surface divergence strength and lifetime is proposed to distinguish the effectiveness of each near-surface motion toward causing interfacial gas transfer. Capillary waves are found to contribute to surface divergence but to have too short a time scale to cause interfacial gas transfer. As wind speed increases, the presence and intensity on the air–water interface of capillary waves and other ineffective near-surface motions is diminished by the rise of turbulent wakes from microscale breaking waves thus causing the disagreement of the surface divergence model’s predicted transfer rates with measurements. A model of air–water gas transfer that combines the surface renewal and surface divergence models is formulated and found to agree with the data from both open-channel flows and wind-driven flows without requiring an empirical coefficient.