While some green water _can_ be caused by Cyanobacteria (unicellular species of blue green algae), there is also green water from green algae, dinoflagellates, golden and yellow-green (incl. diatoms),etc. Wetzel says most BG are filamentous, but most planktonic BG are members of one family ...
and, in some species, the red pigment phycoerythrin. The combination of phycobilin and chlorophyll produces the characteristic blue-green colour from which these organisms derive their popular name. Because of the other pigments, however, many species are actually green, brown, yellow, black, or ...