There are a few ways of killing the moss off. Remember moss is harder to kill than algae due to it is a multicelluar plant. I have seen bakeing soda, zink, and copper used as well as some herbacides but I would caution you about those. Here is some good links.
http://bryophytes.science.oregonstate.edu/page24.htm
http://turfgrassmanagement.psu.edu/c...ontrolmoss.cfm
Steve