Jamieson, Fausset and Brown on Deuteronomy 3:16

16. from Gilead--that is, not the mountainous region, but the town Ramoth-gilead,

even unto the river Arnon half the valley--The word "valley" signifies a wady, either filled with water or dry, as the Arnon is in summer, and thus the proper rendering of the passage will be--"even to the half or middle of the river Arnon" (compare Jos 12:2). This prudent arrangement of the boundaries was evidently made to prevent all disputes between the adjacent tribes about the exclusive right to the water.