Invisible but measurable physical phenomena such as wind speed, temperature, or electrical charge are said to occur at the surface of a solid or liquid. Visible objects, however, rest on the surface. A river or ocean current, for instance, might have a different speed at the surface, which will also affect anything floating on the surface.
Surface states are electronic states which are strongly localized at the surface or interface of a solid. — Robert J. Gale, Spectroelectrochemistry: Theory and Practice, 1988, 136.
This gain of energy at the surface warms the surface. As a result, surface air temperature shows less diurnal range than if there were no heat storage in the soil. The same behavior occurs annually, when heat is stored in soil in warm months and released during cold months. — Gordon B. Bonan, Ecological Climatology: Concepts and Applications, 2002, 185.
High pressure at the surface of the Earth is caused by there being more air in the vertical column from the surface up to the top of the atmosphere than in a column with lower pressure at the surface. — Peter Inness, Understand The Weather: Teach Yourself, 2010.