1. On, or pertaining to, the banks of a stream. (As in riparian vegetation or riparian woodland.)
2. Pertaining to the banks and other adjacent, terrestrial (as opposed to aquatic) environs of freshwater bodies, watercourses, and surface-emergent aquifers (e.g., springs, seeps, oases), whose imported waters provide soil moisture significantly in excess of that otherwise available through local precipitation - soil moisture to potentially support a mesic vegetation distinguishable from that of the adjacent more xeric upland.

Source: Warner and Hendrix. Riparian Resources of the Central Valley and California Desert. 1985. California Department of Fish and Game.