Definition of "deepest"

Most of the Himalayan rivers have been relatively untouched by dams near their sources. Now the two great Asian powers, India and China, are rushing to harness them as they cut through some of the world's deepest valleys.

2013 August 16, John Vidal, “Dams endanger ecology of Himalayas”, in The Guardian Weekly, volume 189, number 10, page 8