I think you have hair algae by the looks of it. I had something similar. While it is short it certainly looks like "turf'" but as it grows out it is definite fine algae that breaks off in the fingers.
I'm starting to win the war with manual removal, Nassarius snails, a blennie and chaeto in a newish tank. My tank literally looked like rolling fields of green. The trick is to get you hands in there.
I run chaeto in the refugium on an alternate cycle. I scrub off any algae starting to get longer than half a cm with a stiff plastic bristled brush. I find that the snails are more inclined to eat it if it is shorter as well. Once the snails give the scrubbed areas a once over I'm finding that not much is growing back, if anything. The chaeto is out-competing new growth. I'm starting to find that any new growth is being dealt with fairly quickly by the snails and blennie because they aren't busy going over a tank full of the stuff.
It's a bit chicken and egg but the more mass the algae has, the more capacity it has to chew up nutrients. Simply removing it and allowing the chaeto to get a foothold by getting to the nutrients first is the key.
Also, beware of dead algae breaking down and causing further nutrient issues.
