Alum, aluminum sulfate, Al2(SO4)3 , is a cationic coagulant which provides a cationic (+) charge to the water. When sufficient amount is added, which can be as little as 250 ppm or up to 1500 ppm, the "iso-electric" point is achieved and solids begin to precipitate. The solids drop to the lake bottom (containing aluminum) and accumulate. The sludge generated is a very light, not easily settled precipitate. Typically when used in drinking water clarification, a flocculant is used to enhance settling. Not a good idea in a lake! There are many factors that affect the "surface tension" of the water; total dissolved solids, total suspended solids, alkalinity, temperature and pH. It is the surface tension difference from lake to lake (in addition to depth) that skiers feel.
Alum is bring used for side stream phosphate removal in Lake Apopka in Florida. The down side is now you have sludge laden with aluminum and phosphate which must be dewatered and trucked out. The dried sludge has tons of phosphate and aluminum that goes to land fill.
Will Alum clarify water? Yes. However, in a "land locked" , non-flowing lake, the sludge accumulates on the lake bed. It may over time become more dense and compact, but it is sludge non the less.
At 1500 ppm dosage, in a million gallons, you would have to add 12, 510 lbs!
Hope this helps.
MWN