Carnen

Carnen — Sindarin for Redwater — was a river that flowed generally southward from the Iron Hills east of the Lonely Mountain until it met the Celduin about 250 Númenórean miles to the south. Its course lay in the boundary region between "The North" (the northwestern region of Middle-earth) and the vast "East" (the area called Rhûn).
Between the time when Thráin I founded the dwarf-kingdom in the Lonely Mountain (in 1999) and the arrival of Smaug (in 2770) the Northmen living between the Celduin and Carnen grew strong and repelled all eastern enemies. This area became depopulated after the arrival of the dragon but again filled with Northmen after Smaug's demise.
For a long time Sauron's allies threatened the borders of the Kingdom of Dale, until during the War of the Ring (around 14 March) the northern host of Sauron crossed the Carnen and drove the forces of King Brand back to Dale.