This would usually be called an elevated riverbed, but I think that's more common when talking about rivers in technical terms. In conversation with non-hydrologists, I'd probably just describe it.
Another term is channelized, but a channelized stream is any that has been artificially directed into a manmade, or human-enhanced channel rather than allowed to flow naturally. Channelized streams usually flow at ground level, but it would also cover the situation you are describing.
Finally, an aqueduct is a manmade elevated channel to carry water for the purpose of drinking water or irrigation. It's been redirected from it's natural channel, sometimes for hundreds of miles. They are often raised far above the ground to provide slope necessary for the water to reach its destination. So while some aqueducts would fit the situation you described, not all tenjougawas would be aqueducts.