A screen on an intake pipe like that can easily plug. There are no great solutions if you insist on no residue going into your pipe, like what may be out in a farm field or yard connected to corrugated tile. The good news is your probably have a very short run of smooth pipe to the outlet and it will stay cleaned out, if the screen ever does become a problem and you want to remove it.That's a LOT of water! We got a ton of rain last night, as I'm sure did many others on INGO.
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Thinking my best bet will just be putting rocks / branches in the discharge valley to slow the waters flow after it exits the discharge.
In two years, can't say I've ever seen the overflow covered by 2" of water and it starting to make its way up the spillway...
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As far as slowing that flow, branches are somewhat temporary, rocks are foreverish.
Have you by chance examined the bottom of the eroded channel? It wouldn't take very many flow events like that to erode it down to bedrock or some type of solid base, and I'm wondering if you're there already and really don't have anything to worry about, except maybe the sides of the channel?
An afterthought...if you do place rocks or something else in that channel and don't also reinforce the side banks, the water is just going to divert from the existing channel and make a new gully in the side banks. Path of least resistance, that is the most downhill.