Dirt Stains or Algae?

What happens when you brush them? If they go away, likely just organic material.

Did you fertilize your lawn? Maybe iron staining from fertilizer. If they don't brush away, put some vitamin C tablets in a sock, crush them up a bit and rub them on the spots...see if that takes care of it.

Does not look like algae, but you can always do this test to confirm. Link-->Overnight Chlorine Loss Test
 
Place 15 to 20 Vitamin C tablets in a sock and crush them. Hold the sock on the stain for 3 to 5 minutes. If the stain vanishes or lightens then it is iron.
 
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