Bringing this forward:
Here is a map of Rhovanion which includes Erebor (The Lonely Mountain) and The Sea of Rhûn.
Please note:
Celduin is the Elvish name for
The River Running
Carnen is the Elvish name for
The Redwater River - which rose from the Iron Hill and whose waters were a rusty reddish-orange from the iron deposits at its source.
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Map
HERE.