A quick, non-biologist's googling suggests that nitrate and ammonium are the limiting factors for most oceanic algae.

I recall there being experiments for areas are iron limited, so they spread iron sulfate and created algae blooms.

I suppose intuitively, if you scoop up a bucket of ocean water, it is not green. If light were the limiting factor you would expect the water to contain lots of light absorbing algae. This does happen in nutrient rich waters, like the sewage lagoons and creeks I grew up near.