A tributary valley whose floor is discordant with the floor of the main valley. Hanging valleys are a hallmark of glacial erosion in mountains. The discordance of the valley floors was one of the arguments used in the early nineteenth century to suggest that rivers did not cut valleys, and the objection was only removed when the role of glacier activity was appreciated. The valley cross-sections were adjusted to the glaciers they held, and it is likely that the glacier surfaces met concordantly (Penck, 1905).
Summary Article: hanging valley from The Dictionary of Physical Geography