Longitudinal profiles of alluvial and bedrock rivers are typically concave up, and the precise shape of their concavity is known to integrate tectonic, climatic, and channel grain size distribution factors. We isolate climatic/hydrologic effects on profile concavity through a spatial analysis of large watersheds with mixed bedrock-alluvial trunk channels spanning a steep climatic/hydrologic gradient in a tectonically stable landscape. Forty watersheds on the eastern American high plains were selected to minimize variability in base level, relief, vegetation, rock type, and drainage area. We calculate stream concavity by two complementary methods: an area-normalized stream concavity index (SCI) and $theta$, the slope of a line regressed through log-log plot of channel slope and basin area. The SCI and $theta$ covary. More importantly, a positive correlation exists between profile concavity and climatic/hydrologic factors such as precipitation intensity and peak annual discharge; however, modeled profile steepness has no correlation to climate or watershed hydrology. We conclude that in tectonically stable settings, higher-intensity rainfall and greater mean annual precipitation lead to more concave profiles. We do not have data to know if the concavity changes reflect primarily bedrock or alluvial (grain size) processes, but generally, a doubling of rainfall intensity on the high plains leads to a tripling in concavity manifest as tens of meters of incision. Such climatically influenced profile concavity could explain some of the often-cited late Cenozoic incision and increase in local relief for the high plains and Rocky Mountains traditionally ascribed to tectonics.