Using radiative reflectance as the discriminatory functional trait, we find scale-free signatures of local functional diversity density of vegetation in river basins, implying a high likelihood of locations with very high diversity relative to the overall diversity of the riparian systems (i.e., riparian diversity hot spots). The spatial series of average local functional diversity exhibits correlation structures that indicate long-range communication of diversity information along river networks. The riparian area of a randomly selected streamlink is found to be exponentially distributed. Our findings suggest that landscape structure and dispersal directionality play crucial roles in determining biodiversity patterns, and thus should be addressed in comprehensive biodiversity theories and fieldwork and conservation campaigns. Finally, the connection between the spectral-group-based functional diversity signatures and those associated with the actual species richness is yet to be verified and quantified; such connection will significantly enhance the importance of the already meaningful signatures reported here.